Question

A rectangular pyramid is shown in the figure. A rectangular pyramid with a base of dimensions 6 inches by 5 inches. The two large triangular faces have a height of 7.8 inches. The two small triangular faces have a height of 8 inches. What is the surface area of the pyramid? 116.8 in2 233.6 in2 58.4 in2 86.8 in2

Answer 1

Answer: 117.8

Explanation:

To find the surface area of a rectangular pyramid, we need to find the area of each face and add them up.

First, we can find the area of the rectangular base:

Area of base = length x width = 6 in x 5 in = 30 in²

Next, we can find the area of each of the four triangular faces. For the two larger triangular faces:

Area of each larger face = 0.5 x base x height = 0.5 x 6 in x 7.8 in = 23.4 in²

And for the two smaller triangular faces:

Area of each smaller face = 0.5 x base x height = 0.5 x 5 in x 8 in = 20 in²

Now we can add up the areas of all the faces to find the total surface area of the pyramid:

Surface area = Area of base + 2 x Area of larger face + 2 x Area of smaller face

Surface area = 30 in² + 2 x 23.4 in² + 2 x 20 in²

Surface area = 117.8 in²

Therefore, the surface area of the rectangular pyramid is 117.8 square inches.

Answer 2

116.8 in^2.

Explanation:

To find the surface area of the rectangular pyramid, we need to find the areas of all the faces and add them together.

The area of the rectangular base is:

Area of base = length x width = 6 in x 5 in = 30 in^2

The area of each of the two large triangular faces is:

Area of triangle = 1/2 x base x height = 1/2 x 6 in x 7.8 in = 23.4 in^2

So, the total area of the two large triangular faces is:

Total area of two large triangular faces = 2 x 23.4 in^2 = 46.8 in^2

The area of each of the two small triangular faces is:

Area of triangle = 1/2 x base x height = 1/2 x 5 in x 8 in = 20 in^2

So, the total area of the two small triangular faces is:

Total area of two small triangular faces = 2 x 20 in^2 = 40 in^2

Therefore, the total surface area of the pyramid is:

Total surface area = Area of base + Total area of two large triangular faces + Total area of two small triangular faces

Total surface area = 30 in^2 + 46.8 in^2 + 40 in^2

Total surface area = 116.8 in^2