Question - Calculating Areas of Base and Lateral Faces of Right Triangular Pyramid
Solution:
The image shows a right triangular pyramid with a square base. The sides of the square base are 4.5 inches, and the slant height (the height of each triangular face, not the height from the base to the apex) is 4.4 inches.Part A of the question asks for the area of the base and the area of each lateral face.To find the area of the base (A_base), we use the formula for the area of a square:\[ A_{\text{base}} = s^2 \]where $$ s $$ is the length of a side of the square. Since the side length is 4.5 inches, we calculate the area as:\[ A_{\text{base}} = (4.5\ \text{in})^2 = 20.25\ \text{in}^2 \]To find the area of each lateral face (A_face), we use the formula for the area of a triangle:\[ A_{\text{face}} = \frac{1}{2} \times \text{base} \times \text{height} \]For the lateral faces, the base is the side of the square (4.5 inches), and the height is the slant height (4.4 inches). The area of each lateral face is:\[ A_{\text{face}} = \frac{1}{2} \times 4.5\ \text{in} \times 4.4\ \text{in} = 9.9\ \text{in}^2 \]So, the area of the base is 20.25 square inches, and the area of each lateral face is 9.9 square inches.
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