Question

Please help 30 points

Answer 1

Answer:

The area of the polygon is 624.5 square feet.

Step-by-step explanation:

The total area of the figure ($A$), in square feet, is the sum of the areas of two triangles and a rectangle, that is:

$A = A_{I}+A_{II}+A_{III}$ (1)

Where:

$A_{I}$ - Area of the big triangle, in square feet.

$A_{II}$ - Area of the small triangle, in square feet.

$A_{III}$ - Area of the rectangle, in square feet.

Then, we expand the formula by using all dimensions presented in the image attached:

$A = \frac{1}{2}\cdot (25\,ft)\cdot (33\,ft-8\,ft) + \frac{1}{2}\cdot (8\,ft)\cdot (43\,ft-35\,ft) + (35\,ft)\cdot (8\,ft)$

$A = 624.5\,ft^{2}$

The area of the polygon is 624.5 square feet.