Answer:
\(42\text{ ft}^2\)
Step-by-step 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.
\(\text{Area of rectangle}=7\text{ ft}\times 3\text{ ft}\)
\(\text{Area of rectangle}=21\text{ ft}^2\)
\(\text{Area of trapezoid}=\frac{6\text{ ft}+3\text{ ft}}{2}\times 4\text{ ft}\)
\(\text{Area of trapezoid}=9\text{ ft}\times 2\text{ ft}\)
\(\text{Area of trapezoid}=18\text{ ft}^2\)
\(\text{Area of triangle}=\frac{2\text{ ft}\times 3\text{ ft}}{2}\)
\(\text{Area of triangle}=3\text{ ft}^2\)
\(\text{Total area of composite figure}=21\text{ ft}^2+18\text{ ft}^2+3\text{ ft}^2\)
\(\text{Total area of composite figure}=42\text{ ft}^2\)
Therefore, the total area of the composite figure is 42 square feet.
