Question

The cloth top of the gazebo in Mr. Chang’s backyard has ripped from weathering. He needs to know the area of the cloth so he can replace it.
A square pyramid with a base of 6 feet by 6 feet. The triangular sides have a height of 5 feet. The height of the pyramid is 4 feet.

How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure?
60
96
120
156

Answer 1

To find the area of the cloth that Mr. Chang needs for the gazebo, we need to calculate the area of the four triangular sides of the square pyramid, as he does not need to replace the cloth at the bottom.

The formula for the area of one triangular side is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this case, the base of each triangular side is equal to the side of the square base of the pyramid (6 feet), and the height of the triangular side is given as 5 feet.

Now, let's calculate the area of one triangular side:

\[
\text{Area} = \frac{1}{2} \times 6 \, \text{feet} \times 5 \, \text{feet} = \frac{1}{2} \times 30 \, \text{square feet} = 15 \, \text{square feet}
\]

Since there are 4 triangular sides, we multiply the area of one triangular side by 4:

\[
\text{Total Area} = 4 \times 15 \, \text{square feet} = 60 \, \text{square feet}
\]

Therefore, Mr. Chang will need **60 square feet** of cloth to replace the ripped top of the gazebo.

So, the answer is:

**60** square feet.