Question - Calculating Area of Square Pyramid and Lateral Faces
Solution:
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.
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