ISASP Grades 6-8 Geometry. Practice it free.

Trapezoid area $= \dfrac{1}{2}(b_1 + b_2) \cdot h = \dfrac{1}{2}(5 + 6) \cdot 4 = \dfrac{1}{2}(11) \cdot 4 = 22$.

The area of a rhombus is half the product of the diagonals: $\dfrac{1}{2} \cdot 8 \cdot 5 = 20\text{ in}^{2}\textsf{.}$

$\Delta x = 3$, $\Delta y = 4$. $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.

The scale factor from $\triangle GHI$ to $\triangle JKL$ is $\dfrac{48}{16} = 3\textsf{.}$ Corresponding sides scale by $3\textsf{,}$ so $JK = 5 \cdot 3 = 15\textsf{.}$

Let each congruent angle measure $x^{\circ}$. Then $2x + 118.6 = 180$, so $x = \dfrac{180 - 118.6}{2} = 30.7^{\circ}$.

A hexagon has $6$ sides: $(6-2) \times 180 = 720°$.

The legs are $11$ and $60$. By the Pythagorean theorem, $11^{2} + 60^{2} = 121 + 3{,}600 = 3{,}721$, so the hypotenuse is $\sqrt{3{,}721} = 61$.

$17^{2} - 8^{2} = 289 - 64 = 225$, so the other leg is $\sqrt{225} = 15\textsf{.}$