Question

The total area of the polygon is 176 square feet. Find the value of x.

Answer 1

The answer is six to one of the sides

Explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 =

=

= 4x square feet

Area of rectangle 2 = Length × Width

= 16 × 8

= 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x =

x = 6 ft

Answer 2

x = 6 ft

Explanation:

Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3

Area of triangle 1 = Area of triangle 3 =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(x)(8)`

= 4x square feet

Area of rectangle 2 = Length × Width

= 16 × 8

= 128 square feet

Total area of the given polygon = 4x + 128 + 4x

176 = 8x + 128

8x = 176 - 128

x =
`(48)/(8)`

x = 6 ft