Big Ideas Math: Modeling Real Life, Grade 7
BI
Big Ideas Math: Modeling Real Life, Grade 7 View details
Cumulative Practice

Exercise 7 Page 452

Add the area of the square base to the area of the lateral faces.

H

A square pyramid has one square base and four triangular faces. Let's take a look at the given diagram.

pyramid

We can use the net of this 3-dimensional shape to find its surface area.

The surface area of a pyramid is the sum of the area of the base and the areas of the lateral faces. Let's calculate the area of the base and the faces one at a time. Then we can add them together.

Base

Looking at the net of this solid, the base is a square with a side length of 6 inches. The square's area is the square of the side length. Therefore, the area of our base is 6^2 = 36 square inches.

Lateral Faces

Because the base of the pyramid is an square, we know that all four of the lateral faces are congruent. Since they are all exactly the same size, we only need to calculate the area of one of the faces. We can see in the diagram that the base of the lateral side is 6 inches and the height is 8 inches. We can substitute these values into the formula for the area of a triangle.
A=1/2bh
A=1/2( 6)( 8)
Evaluate right-hand side
A=1/2(48)
A=48/2
A=24
The area of one lateral face is 24 square inches. Let's add this value 4 times to get the area of all four lateral faces combined. Surface Area of the Four Lateral Faces 24+24+24+24= 96square inches

Surface Area of the Pyramid

Finally, to find the surface area of the square pyramid, we will add the area of the base and the area of the four lateral faces. Surface Area of the Square Pyramid 36+ 96=132square inches Therefore, the correct option is H.