A $5\mathrm{.}7-$m$-$long simply supported timber beam carries a uniformly distributed load of $13\mathrm{.}5k\frac{N}{m}.$ The cross$-$sectional dimensions of the beam are shown in the second figure.

Assume $x=1\mathrm{.}4m,b=80mm,d=240mm,y_H=39mm$ and $y_K=67mm.$

At point $H$ of the cross$-$section, the first moment of area $Q_H$ is most nearly:

A$.457000m{m}^3$

B$.515000m{m}^3$

C$.582000m{m}^3$

D$.685000m{m}^3$

E$.739000m{m}^3$

F$.853000m{m}^3$

G$.937000m{m}^3$

H$.1040000m{m}^3$

I. $1120000m{m}^3$

J$.1250000m{m}^3$

At section $a-a,$ the magnitude of the shear stress at point $H$ of the cross$-$section is most nearly:

A$.0\mathrm{.}523$MPa

B$.0\mathrm{.}889$MPa

C$.1\mathrm{.}37$MPa

D$.1\mathrm{.}85$MPa

E$.2\mathrm{.}29$MPa

F$.2\mathrm{.}73$MPa

G$.3\mathrm{.}18$MPa

H$.3\mathrm{.}57$MPa

I. $3\mathrm{.}94$MPa

J$.4\mathrm{.}21$MPa