Find the surface area of a rectangular pyramid with these measurements: l = 8 yd., w = 4 yd., and h = 2 yd.(1 point)
Responses
43.31 yd.2
43.31 yd. 2
55.55 yd.2
55.55 yd. 2
72.52 yd.2
72.52 yd. 2
66 yd.2
To find the surface area of a rectangular pyramid, we need to find the area of each face and add them together.
The base of the pyramid is a rectangle with length 8 yd and width 4 yd. The area of the base is 8 * 4 = 32 square yards.
The triangular faces are all congruent, so we just need to find the area of one of them. We can find the height of the triangular face by using the Pythagorean theorem. The hypotenuse of the triangle is the slant height of the pyramid, which is the height of the pyramid (2 yd). The base of the triangle is the width of the rectangle (4 yd). By using the Pythagorean theorem, we can solve for the height of the triangular face:
( height of triangle )^2 + (4/2)^2 = 2^2
( height of triangle )^2 + 2^2 = 2^2
( height of triangle )^2 = 0
(height of triangle) = 0
Since the height of the triangle is 0, the area of the triangle is also 0.
Therefore, the surface area of the rectangular pyramid is just the area of the base, which is 32 square yards.
The correct answer is 32 yd.2