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mathematics
holt mcdougal larson geometry

Questions and Answers of Holt McDougal Larson Geometry

Basaltic columns are geological formations that result from rapidly cooling lava. The Giant's Causeway in Ireland, pictured here, contains many hexagonal columns. Suppose that one of the columns is
Decide whether the statement is true or false. Explain.The area of a regular n-gon of fixed radius r increases as n increases.
A motorized scooter has a chain drive. The chain goes around the front and rear sprockets.a. About how long is the chain? Explain. b. Each sprocket has teeth that grip the chain. There are 76 teeth
Decide whether the statement is true or false. Explain.The apothem of a regular polygon is always less than the radius.
Find the circumference of a circle inscribed in a rhombus with diagonals that are 12 centimeters and 16 centimeters long. Explain.
Decide whether the statement is true or false. Explain.The radius of a regular polygon is always less than the side length.
The eye of a hurricane is a relatively calm circular region in the center of the storm. The diameter of the eye is typically about 20 miles. If the eye of a hurricane is 20 miles in diameter, what is
As shown, a measuring wheel is used to calculate the length of a path. The diameter of the wheel is 8 inches. The wheel rotates 87 times along the length of the path. About how long is the path?
Over 2000 years ago, the Greek scholar Eratosthenes estimated Earth's circumference by assuming that the Sun's rays are parallel. He chose a day when the Sun shone straight down into a well in the
A square is inscribed in a circle. The same square is also circumscribed about a smaller circle. Draw a diagram. Find the ratio of the area of the large circle to the area of the small circle.
A watch has a circular face on a background that is a regular octagon. Find the apothem and the area of the octagon. Then find the area of the silver border around the circular face. 0.2 cm 2 + 6 1 cm
Predict which figure has the greatest area and which has the smallest area. Check by finding the area of each figure. a. 13 in. b. 15 in. 18 in. C. 9 in.
Use a ruler and compass.a. Draw AB with a length of 1 inch. Open the compass to 1 inch and draw a circle with that radius. Using the same compass setting, mark off equal parts along the circle. Then
A new typeface has been designed to make highway signs more readable. One change was to redesign the form of the letters to increase the space inside letters.a. Estimate the interior area for the old
The table shows how students get to school.a. Explain why a circle graph is appropriate for the data. b. You will represent each method by a sector of a circle graph. Find the central angle to use
A square with side length 6 units is inscribed in a circle so that all four vertices are on the circle. Draw a sketch to represent this problem. Find the circumference of the circle.
Suppose AB is divided into four congruent segments, and semicircles with radius r are drawn.What is the sum of the four arc lengths if the radius of each arc is r? A Ar- A-r- B B В
Find the area of a circle with radius r. Round to the nearest hundredth. r = 6 cm
Suppose AB is divided into four congruent segments, and semicircles with radius r are drawn. Suppose that AB is divided into n congruent segments and that semicircles are drawn, as shown. What will
Find the area of a circle with radius r. Round to the nearest hundredth. دن | طر r = 8 mi 4
Semicircles with diameters equal to the three sides of a right triangle are drawn, as shown. Prove that the sum of the areas of the two shaded crescents equals the area of the triangle.
The area of a circular pond is about 138,656 square feet. You are going to walk around the entire edge of the pond. About how far will you walk? Give your answer to the nearest foot.
Triangle DEG is isosceles with altitude DF. Find the given measurement. Explain your reasoning. m2 DFG
Triangle DEG is isosceles with altitude DF. Find the given measurement. Explain your reasoning. FG
Assume that each honeycomb cell is a regular hexagon. The distance is measured through the center of each cell.a. Find the average distance across a cell in centimeters. b. Find the area of a
Triangle DEG is isosceles with altitude DF. Find the given measurement. Explain your reasoning. m/ FDG
You want to make two wooden trivets, a large one and a small one. Both trivets will be shaped like regular pentagons. The perimeter of the small trivet is 15 inches, and the perimeter of the large
Find the area of a circle with radius r. Round to the nearest hundredth. r = 12 in. 8
Show that a regular hexagon can be divided into six equilateral triangles with the same side length.
A circular pizza with a 12 inch diameter is enough for you and 2 friends. You want to buy pizza for yourself and 7 friends. A 10 inch diameter pizza with one topping costs $6.99 and a 14 inch
Sketch the indicated figure. Draw all of its lines of symmetry. Regular hexagon
Find the area of a circle with radius r. Round to the nearest hundredth.r = 4.2 in.
Sketch the indicated figure. Draw all of its lines of symmetry. Isosceles trapezoid
Use a piece of string that is 60 centimeters long.a. Arrange the string to form an equilateral triangle and find the area. Next form a square and find the area. Then do the same for a regular
Two regular polygons both have n sides. One of the polygons is inscribed in, and the other is circumscribed about, a circle of radius r. Find the area between the two polygons in terms of n and r.
A jar contains 10 red marbles, 6 blue marbles, and 2 white marbles. Find the probability of the event described.You randomly choose one red marble from the jar, put it back in the jar, and then
A jar contains 10 red marbles, 6 blue marbles, and 2 white marbles. Find the probability of the event described.You randomly choose one blue marble from the jar, keep it, and then randomly choose one
Graph ΔABC. Then find its area. A(2, 2), B(9, 2), C(4, 16)
Graph ΔABC. Then find its area. A(-8, 3), B(-3, 3), C(-1, -10)
In Exercises 1-4, use the diagram shown.Identify a central angle of the polygon. G A E 5.5 8 6.8 F B D C
In Exercises 1-4, use the diagram shown.Identify the center of regular polygon ABCDE. G A E 8 5.5 F 6.8 B D C
Copy and complete: A _?_ of a circle is the region bounded by two radii of the circle and their intercepted arc.
In ⊙P shown at the right, ∠QPR ≅ ∠RPS. Find the indicated measure. mQR
Copy and complete the table of ratios for similar polygons. Ratio of corresponding side lengths ? Ratio of perimeters 20:36 = ? Ratio of areas ?
Copy and complete the table of ratios for similar polygons. Ratio of corresponding side lengths 6:11 Ratio of perimeters ? Ratio of areas ?
Corresponding lengths in similar figures are given. Find the ratios (red to blue) of the perimeters and areas. Find the unknown area. 15 cm, A = 240 cm² 20 cm
Find the area of the rhombus or kite. -60- 50
Corresponding lengths in similar figures are given. Find the ratios (red to blue) of the perimeters and areas. Find the unknown area. A=2 ft² 6 ft 2 ft
Corresponding lengths in similar figures are given. Find the ratios (red to blue) of the perimeters and areas. Find the unknown area. A = 40 yd² 5 yd 3 yd
Find the area of the rhombus or kite. # -21- 18
Corresponding lengths in similar figures are given. Find the ratios (red to blue) of the perimeters and areas. Find the unknown area. 7 in. A = 210 in.² 9 in.
The perpendicular distance between the bases of a trapezoid is called the ___?___ of the trapezoid.
Find the area of the rhombus or kite. -48- T 16 1
Sketch a kite and its diagonals. Describe what you know about the segments and angles formed by the intersecting diagonals.
The ratio of the areas of two similar figures is given. Write the ratio of the lengths of corresponding sides. Ratio of areas = 49:16
Two regular n-gons are similar. The ratio of their side lengths is 3:4. Do you need to know the value of n to find the ratio of the perimeters or the ratio of the areas of the polygons? Explain.
Find the area of the rhombus or kite. -19- 10
Find the area of the rhombus or kite. 4 2 5 #
Describe and correct the error in finding the area. 13 cm 14 cm 12 cm 19 cm A = 1/(13)(14 +19) = 214.5 cm² X
The ratio of the areas of two similar figures is given. Write the ratio of the lengths of corresponding sides. Ratio of areas = 16:121
Find the area of the rhombus or kite. 12 15
The lengths of the bases of a trapezoid are 5.4 centimeters and 10.2 centimeters. The height is 8 centimeters. Draw and label a trapezoid that matches this description. Then find its area.
The ratio of the areas of two similar figures is given. Write the ratio of the lengths of corresponding sides. Ratio of areas = 121:144
Use the given area to find XY. UVWXYLMNPQ A = 198 in.² W U V Y X L' A = 88 in.² N M Q P 10 in.
Use the given area to find XY. A Δ DEF ~ Δ ΧΥΖ - D 4 cm E X F A = 7cm² Z A = 28 cm² Y
In the diagram, Rectangles DEFG and WXYZ are similar. The ratio of the area of DEFG to the area of WXYZ is 1:4. Describe and correct the error in finding ZY. D G 12 E W FZ ZY = 4(12) = 48 X x
Describe and correct the error in finding the area. 12 cm =(12)(21) = 126 cm² 5 cm 16 cm x
Use the given information to find the value of x. Area = 300 m² X 20 m 10 m
One diagonal of a rhombus is three times as long as the other diagonal. The area of the rhombus is 24 square feet. What are the lengths of the diagonals? A 8 ft, 11 ft B 4 ft, 12 ft Ⓒ 2 ft, 6 ft D
Use the given information to find the value of x. Area = 108 ft² X 22 ft 14 ft
Find the area of the figure. y 4 x
Use the given information to find the value of x. Area = 100 yd² -X- T 10 yd
Find the area of the figure. y 1 X
Explain why the red and blue triangles are similar. Find the ratio (red to blue) of the areas of the triangles. Show your steps. D₁ P F E 10 m L A = 294 m² M 21 m N
Explain why the red and blue triangles are similar. Find the ratio (red to blue) of the areas of the triangles. Show your steps. T Y √3 yd+ X + U W 30° V
Find the area of the figure. Ay 4 X
Regular pentagon QRSTU has a side length of 12 centimeters and an area of about 248 square centimeters. Regular pentagon VWXYZ has a perimeter of 140 centimeters. Find its area.
Two rectangular banners from this year's music festival are shown. Organizers of next year's festival want to design a new banner that will be similar to the banner whose dimensions are given in the
Rhombuses MNPQ and RSTU are similar. The area of RSTU is 28 square feet. The diagonals of MNPQ are 25 feet long and 14 feet long. Find the area of MNPQ. Then use the ratio of the areas to find the
You need 20 pounds of grass seed to plant grass inside the baseball diamond shown. About how many pounds do you need to plant grass inside the softball diamond?A. 6 B. 9C. 13 D. 20 60
In Exercises 19 and 20, copy and complete the statement using always, sometimes, or never. Explain your reasoning.Doubling the side length of a square _?_ doubles the area.
In the diagram shown at the right, ABCD is a parallelogram and BF = 16. Find the area of ▱ABCD. Explain your reasoning. A 10 E 8 B 8 F 3 G C 9 H
A student wants to show that the students in a science class prefer mysteries to science fiction books. Over a two month period, the students in the class read 50 mysteries, but only 25 science
In Exercises 19 and 20, copy and complete the statement using always, sometimes, or never. Explain your reasoning.Two similar octagons _?_ have the same perimeter.
Use the diagram shown at the right.a. Name as many pairs of similar triangles as you can. Explain your reasoning. b. Find the ratio of the areas for one pair of similar triangles. c. Show two ways
The sides of ΔABC are 4.5 feet, 7.5 feet, and 9 feet long. The area is about 17 square feet. Explain how to use the area of ΔABC to find the area of a ΔDEF with side lengths 6 feet, 10 feet, and
As shown, a baseball stadium's playing field is shaped like a pentagon. To find the area of the playing field shown at the right, you can divide the field into two smaller polygons.a. Classify the
Rectangles ABCD and DEFG are similar. The length of ABCD is 24 feet and the perimeter is 84 feet. The width of DEFG is 3 yards. Find the ratio of the area of ABCD to the area of DEFG.
The windshield in a truck is in the shape of a trapezoid. The lengths of the bases of the trapezoid are 70 inches and 79 inches. The height is 35 inches. Find the area of the glass in the windshield.
Use the triangle area formula and the triangles in the diagram to write a plan for the proof. Show that the area A of the kite shown is dd₂. P Q -d₂- S T T R d₁ I
A new patio will be an irregular hexagon. The patio will have two long parallel sides and an area of 360 square feet. The area of a similar shaped patio is 250 square feet, and its long parallel
Use the triangle area formula and the triangles in the diagram to write a plan for the proof. Show that the area A of the trapezoid shown is ¹⁄h(b₁ + b₂). S P РА h b₂ b₁ Q R
Solve for the indicated variable. Write a reason for each step. =bh; solve for h 2 A=
Use graph paper for parts (a) and (b).a. Draw a triangle and label its vertices. Find the area of the triangle. b. Mark and label the midpoint of each side of the triangle. Connect the midpoints
Solve for the indicated variable. Write a reason for each step. P = 2l + 2w; solve for w
James A. Garfield, the twentieth president of the United States, discovered a proof of the Pythagorean Theorem in 1876. His proof involved the fact that a trapezoid can be formed from two congruent
How is the area of a trapezoid affected if you double the height but keep the lengths of the bases unchanged? if you keep the height unchanged but double the lengths of the bases? Explain.
Solve for the indicated variable. Write a reason for each step. drt; solve for t
The ratio of the areas of two similar polygons is 9:6. Draw two polygons that fit this description. Find the ratio of their perimeters. Then write the ratio in simplest radical form.
You are creating a kite-shaped logo for your school's website. The diagonals of the logo are 8 millimeters and 5 millimeters long. Find the area of the logo. Draw two different possible shapes for

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