Exercise 2 Page 450

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.

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 1 inches. The square's area is a square of the side length. Therefore, the area of our base is 1^2 = 1 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 1 inch and the height is 2 inches. We can substitute these values into the formula for the area of a triangle.

A=1/2bh

SubstituteII

b= 1, h= 2

A=1/2( 1)( 2)

Multiply

A=1/2(2)

FracMultDenomToNumber

a/2* 2 = a

A=1

The area of one lateral face is 1 square inch. Let's add this value 4 times to get the area of all four lateral faces combined. Surface Area of the Four Lateral Faces 1+1+1+1= 4square 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 1+ 4=5square inches

Hints

Check the answer

Base

Lateral Faces

Surface Area of the Pyramid