6 ft How many square feet of outdoor carpet will we need for this hole? 11 ft 7 ft 2 ft 3 ft

Question

asked Jan 19, 2017 111k views

2 Answers

Grijesh Chauhan · Answer 1 · 2017-01-24T04:19:34+0000

Answer:

$42\text{ ft}^2$

Explanation:

We have been given an image of a composite figure and we are asked to find the carpet needed to cover the hole.

We will divide our given figure in 3 parts as shown in the attachment.

The area of our composite figure will be equal to area of a trapezoid plus area of rectangle plus are of triangle.

$\text{Area of rectangle}=7\text{ ft}* 3\text{ ft}$

$\text{Area of rectangle}=21\text{ ft}^2$

$\text{Area of trapezoid}=\frac{6\text{ ft}+3\text{ ft}}{2}* 4\text{ ft}$

$\text{Area of trapezoid}=9\text{ ft}* 2\text{ ft}$

$\text{Area of trapezoid}=18\text{ ft}^2$

$\text{Area of triangle}=\frac{2\text{ ft}* 3\text{ ft}}{2}$

$\text{Area of triangle}=3\text{ ft}^2$

$\text{Total area of composite figure}=21\text{ ft}^2+18\text{ ft}^2+3\text{ ft}^2$

$\text{Total area of composite figure}=42\text{ ft}^2$

Therefore, the total area of the composite figure is 42 square feet.