Question

A designer is creating a rug for an oddly shaped room. His design for the rug is shown below. If each blue square represents 1 square foot,how much cloth will the tailor need for the rug.

(answer is NOT 53!)

Answer 1

44 square feet of the rug will be required.

Explanation:

It's a composite figure having one trapezoid and one triangle.

Area of this composite figure = Area of the trapezoid + Area of the triangle

A =
`(1)/(2)(b_(1)+b_(2))h_(1)+(1)/(2)(b)(h_(2))`

Here
`b_(1)` and
`b_(2)` are the bases of trapezoid

And
`h_(1)` = distance between these bases

b = base of the triangle

`h_(2)` = height of the triangle

Area of the figure =
`(1)/(2)(5+7)(5)+(1)/(2)(7)(4)`

= 30 + 14

= 44 square feet

Therefore, 44 square feet of the rug will be required.