Calculating Area of Square Pyramid and Lateral Faces
The image shows a square pyramid with a slant height of 4.4 inches and a base edge length of 4.5 inches. We are asked to solve for the area of the base and the area of each lateral face.
Part A: What is the area of the base?
Since the base of the pyramid is a square, the area A of a square is given by the formula \( A = s^2 \) where s is the length of a side. Given that s = 4.5 inches, the area of the base is:
\[ A = 4.5^2 = 20.25 \]
\[ A = 20.25 \text{ square inches} \]
The area of the base is therefore 20.25 square inches.
Part A also asks for the area of each lateral face. Each lateral face is a triangle with a base of 4.5 inches and a slant height of 4.4 inches which acts as the altitude in this situation. The area A of a triangle is given by the formula \( A = \frac{1}{2}bh \) where b is the base and h is the height (altitude) of the triangle.
Using the provided measurements, the area of one triangular lateral face is:
\[ A = \frac{1}{2} \times 4.5 \times 4.4 \]
\[ A = \frac{1}{2} \times 19.8 \]
\[ A = 9.9 \]
\[ A = 9.9 \text{ square inches} \]
Thus, the area of each lateral face is 9.9 square inches.
