Question

It takes 24 feet of fence to surround a square piece of land in Sam's backyard. Sam wants to plant flowers everywhere but on the diagonal sidewalk (shaded in the diagram attached). Note that there is 1 foot of sidewalk along two sides of the square as indicated in the diagram attached. What is the area of the sidewalk?

Answer 1

since you know the perimeter is 24, divide that by 4 to get 6 and that is the length of the sides. use that to find the areas of both triangles. the areas are 18 and 12.5. add those to get 30.5 and subtract that from 36 (the area of the whole square) to get 5.5, which is your answer

Answer 2

Option B. 5.5 ft²

Explanation:

Perimeter of the square piece of land = length of fence required

4(length of a side of the square) = 24 ft

Length of a side = 6 ft

Area of the square land = (Side)²

= 6²

= 36 square ft

Area of the side walk = Area of the square - [Area of two triangles separated by the sidewalk]

= 36 - [
`(1)/(2)(\text{Area of the square})+(1)/(2)(\text{Base})\tmes (\text{height})`]

= 36 - [
`(36)/(2)+(1)/(2)(6-1)(6-1)`]

= 36 - (18 + 12.5)

= 36 - 30.5

= 5.5 ft²

Therefore, Option B. is the correct answer.