Question

Please help 30 points

Answer 1

The area of the polygon is 624.5 square feet.

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 = (1)/(2)\cdot (25\,ft)\cdot (33\,ft-8\,ft) + (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.