Answer :
The lateral area of the regular pyramid is 1.69 sq ft to 3 significant digits. The correct answer is option c. The lateral area of a pyramid refers to the combined surface area of all the triangular faces excluding the base.
To calculate the lateral area, we need to determine the area of each triangular face and then sum them up. In this case, we are given the base perimeter, which is 4' 6" or 54 inches. Since it is a regular pyramid, all the triangular faces are congruent, and each face is an isosceles triangle. We can divide the base perimeter by the number of sides of the base to find the length of each side, which is 54 inches divided by 4, resulting in 13.5 inches.
To find the area of each triangular face, we can use the formula A = 0.5 * base * height, where the base is the length of each side and the height is the slant height. Plugging in the values, we get A = 0.5 * 13.5 inches * 9.00 inches = 60.75 square inches. To convert this to square feet, we divide by 144 (since there are 144 square inches in a square foot), resulting in approximately 0.421875 square feet. Since there are four identical triangular faces, we multiply this value by 4 to get the total lateral area, which is approximately 1.6875 square feet or 1.69 sq ft when rounded to 3 significant digits. Therefore, the correct answer is option c.
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