1 point Find the surface area of each pyramid. Round your answers to the nearest tenth, if necessary . (MC) 11.1 yd 7yd 4.8yd A) 254.74y * d ^ 2 C) 301.1y * d ^ 2 B) 211.05 yd D) 278.25y * d ^ 2
To find the surface area of a pyramid, we need to find the area of the base and the area of the four triangular faces.
First, let's find the area of the base which is a rectangle: A = l * w
A = 11.1 * 7 = 77.7 yd^2
Next, let's find the area of the triangular faces. The slant height of the pyramid can be found using the Pythagorean Theorem: l = sqrt( (1/2 * base)^2 + height^2 )
l = sqrt( (1/2 * 11.1)^2 + 4.8^2 )
l = sqrt( 30.765 + 23.04 )
l ≈ sqrt( 53.805 )
l ≈ 7.34 yd
The area of each triangular face is 1/2 * base * height: A_triangle = 1/2 * 11.1 * 7.34 = 40.747 yd^2
Since there are four faces, the total area of the triangular faces is 4 * 40.747 = 162.988 yd^2
Finally, we find the total surface area by adding the area of the base and the area of the triangular faces:
Total surface area = base area + 4 * triangular face area
Total surface area = 77.7 + 162.988
Total surface area ≈ 240.688 yd^2
Therefore, rounding to the nearest tenth, the surface area of the pyramid is approximately 240.7 yd^2.
The closest answer choice is B) 211.05 yd.