Question

ASAP PLEASE!! Find the area of the polygon.

A. 59 square units
B. 65 square units
C. 72 square units
D. 83 square units

Answer 1

Answer:

65 square units

Step-by-step explanation:

The easiest way to calculate the area of the given irregular polygon is to divide the shape into a triangle and a trapezoid (see attached diagram).

Area 1: triangle

$\begin{aligned}\textsf{Area of a triangle} & = \sf \dfrac{1}{2} \times base \times height\\ & = \sf \dfrac{1}{2} \times SU \times height\\& = \sf \dfrac{1}{2} \times 8 \times 4\\& = \sf 16\:\:square\:units\end{aligned}$

Area 2: trapezoid

$\begin{aligned}\textsf{Area of a trapezoid} & = \sf \dfrac{1}{2} (base_a+base_b) \times height\\& = \sf \dfrac{1}{2}(SU+RQ) \times RS\\& = \sf \dfrac{1}{2} (8+6) \times 7\\ & = \sf \dfrac{1}{2}(14) \times 7\\ & = \sf 7 \times 7\\& = \sf 49\:\:square\:units\end{aligned}$

Area of the polygon

$\begin{aligned}\textsf{Area of the polygon} & = \textsf{Area of triangle}+\textsf{Area of trapezoid}\\& = \sf 16 + 49\\& = \sf 65\:square\:units \end{aligned}$

Therefore, the area of the polygon is 65 square units.

Learn more about composite shapes here:

https://brainly.com/question/27744042

https://brainly.com/question/27743608