FAST Grade 8 Geometric Reasoning and Measurement. Practice it free.

$V = 2 \times 4 \times 9 = 72$.

The two congruent angles share the remainder equally: $\dfrac{180^{\circ} - 52.6^{\circ}}{2} = 63.7^{\circ}$.

A pentagon has $5$ sides: $(5-2) \times 180 = 540°$.

Let the missing leg be $x$. Then $x^{2} + 18^{2} = 30^{2}$, so $x^{2} = 30^{2} - 18^{2} = 900 - 324 = 576$ and $x = \sqrt{576} = 24$.

$20^{2} + 21^{2} = 400 + 441 = 841$, so the hypotenuse is $\sqrt{841} = 29\textsf{.}$

The walk forms the legs of a right triangle: $\sqrt{8^{2} + 15^{2}} = \sqrt{64 + 225} = \sqrt{289} = 17$ blocks.

Area $A = \ell w$, so $120 = 8w$ and $w = 15$. The diagonal is the hypotenuse of a right triangle with legs $8$ and $15$: $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}$

The sum of the interior angles of a triangle is $180^{\circ}\textsf{.}$ So $m\angle P = 180^{\circ} - 64^{\circ} - 64^{\circ} = 52^{\circ}\textsf{.}$