Cumulative Practice
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H
A square pyramid has one square base and four triangular faces. Let's take a look at the given diagram.
We can use the net of this 3-dimensional shape to find its surface area.
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.
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.
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
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.