Question

The square pyramid below represents a tent that Wayne is making. The sides of the tent will be covered in blue fabric, and the base of the tent will be covered in brown fabric. Find the surface area that will be covered in each color of fabric. (Base: 3m², Height: 4.5m)

A. Blue fabric: 22.5 m², Brown fabric: 13.5 m²
B. Blue fabric: 13.5 m², Brown fabric: 22.5 m²
C. Blue fabric: 27 m², Brown fabric: 18 m²
D. Blue fabric: 18 m², Brown fabric: 27 m²

Answer 1

To find the surface area covered in each color of fabric for the square pyramid tent, calculate the lateral area and the area of the base. The lateral area is 13.5m² and the area of the base is 3m².

Step-by-step explanation:

To find the surface area covered in each color of fabric, we first need to find the lateral area of the square pyramid. The lateral area is the sum of the areas of all the triangular faces of the pyramid. The base of the triangular face is the same as the side length of the square base, which is 3m. The height of the triangular face is the same as the height of the pyramid, which is 4.5m. Therefore, the lateral area is calculated as:

Lateral area = (0.5) * (base * height) * number of triangular faces

Lateral area = (0.5) * (3 * 4.5) * 4

Lateral area = 13.5m²

Since the sides of the tent will be covered in blue fabric, the surface area covered in blue fabric is equal to the lateral area, which is 13.5m².

The base of the tent will be covered in brown fabric. The area of the square base is given as 3m², so the surface area covered in brown fabric is 3m².

Therefore, the surface area covered in each color of fabric is:

Blue fabric: 13.5m²

Brown fabric: 3m²