Surface Area of Rectangular Pyramids Quick Check

Question

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Question
Use the image to answer the question.

A rectangle has 4 triangles connected to it. One triangle is attached to each side of the rectangle. The rectangle is labeled base. The triangle on the top is labeled face 1. The triangle on the right is labeled face 2. The triangle on the bottom is labeled face 1. The triangle on the left is labeled face 2.

Use the net to derive a formula for the surface area (SA) of the rectangular pyramid.

(Use the variable Abase
for the area of the base, Aface 1
for the area of face 1, and Aface 2
for the area of face 2.)

Responses

SA=2×Aface 1+2×Aface 2
cap s cap A is equal to 2 times cap A sub f A c e 1 plus 2 times cap A sub f A c e 2

SA=Abase+2×Aface 1+2×Aface 2
cap s cap A is equal to cap A sub b A s e plus 2 times cap A sub f A c e 1 plus 2 times cap A sub f A c e 2

SA=2×Abase+2×Aface 1+2×Aface 2
cap s cap A is equal to 2 times cap A sub b A s e plus 2 times cap A sub f A c e 1 plus 2 times cap A sub f A c e 2

SA=Abase+Aface 1+Aface 2
cap s cap A is equal to cap A sub b A s e plus cap A sub f A c e 1 plus cap A sub f A c e 2

Answer 1

SA=Abase+2×Aface 1+2×Aface 2
(cap S Cap A) is equal to (cap A sub base) plus 2 times (cap A sub face 1) plus 2 times (cap A sub face 2)

Answer 2

Use the image to answer the question.

An illustration shows a pyramid with a square base. The side of the base is labeled 15 feet. The perpendicular height denoted by a right angle symbol on the lateral face from the apex to the base is labeled 9.9 feet.

Solve for the surface area of the square pyramid.

(1 point)
Responses

522 ft.2
522 ft. squared

819 ft.2
819 ft. squared

148.5 ft.2
148.5 ft. squared

299.25 ft.2
299.25 ft. squared
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Answer 3

To find the surface area of the square pyramid, we need to calculate the area of the base (which is a square) and the area of all the four triangular faces.

1. The area of the base (square) = side length * side length = 15 ft * 15 ft = 225 sq ft.

2. Now, for each triangular face:
- The base edge is 15 ft (same as the side of the square base).
- The height of each triangular face can be found using the Pythagorean theorem:
height = sqrt((side length / 2)^2 + height^2) = sqrt((15 / 2)^2 + 9.9^2) = sqrt(7.5^2 + 9.9^2) = sqrt(56.25 + 98.01) = sqrt(154.26) = approximately 12.42 ft.
- The area of each triangular face = 0.5 * base * height = 0.5 * 15 ft * 12.42 ft = 93.15 sq ft.

3. Since there are four triangular faces, the total area of all the faces = 4 * 93.15 sq ft = 372.6 sq ft.

The total surface area of the square pyramid = Area of the base + Total area of all faces = 225 sq ft + 372.6 sq ft = 597.6 sq ft.

Therefore, none of the provided options matches the calculated result. The correct surface area is approximately 597.6 sq ft.