Question - Calculating Areas of Pyramid's Base and Lateral Faces
Solution:
The image displays a math problem that involves finding the areas of different parts of a pyramid. It already contains a calculation for the area of the base, as well as the calculation and answer for the area of one of the lateral faces. Looking at the image, we can see that the base is a square because all sides are of equal length (4.5 in). The area of a square is found using the formula A = s^2, where s is the length of a side of the square. The calculation in the image is correct: A = (4.5 in)^2 = 20.25 in^2. That is the area of the base of the pyramid.For a lateral face, which is a triangle in this case, the area is calculated using the formula A = 1/2 * b * h, where b is the base of the triangle and h is the height. From the image, it shows they've used one side of the square base as the base of the triangle (b = 4.5 in) and the slant height of the pyramid as the height of the triangle (h = 7 in). The calculation for one lateral face is A = 1/2 * (4.5 in) * (7 in) = 15.75 in^2. This is also correct as shown in the image.To sum it up:- The area of the base (A_base) is 20.25 in^2.- The area of one lateral face (A_lateral) is 15.75 in^2.Since a pyramid with a square base has four identical lateral faces, if you wanted to find the total area of all the lateral faces, you would multiply the area of one lateral face by four (4 * 15.75 in^2 = 63 in^2). The image does not show this total calculation, but I included it here for a more comprehensive understanding.
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