Question

sarah is designing a triangular pyramid made of all glass to go on top of a building. all of the faces of the pyramid have a height of 17 feet and a base of 20 feet.
image: a blue triangular net with four smaller triangles (figure not drawn to scale)
note: figure is not drawn to scale.
how much glass is needed?
a. 340 sq ft
b. 680 sq ft
c. 1,360 sq ft
d. 2,040 sq ft

Explanation:

Step1: Recall the formula for the area of a triangle

The area of a triangle is given by \( A = \frac{1}{2} \times b \times h \), where \( b \) is the base and \( h \) is the height.

Step2: Calculate the area of one triangular face

Given \( b = 20 \) feet and \( h = 17 \) feet, substitute into the formula:
\( A_{one} = \frac{1}{2} \times 20 \times 17 \)
\( A_{one} = 10 \times 17 = 170 \) square feet.

Step3: Determine the number of triangular faces in a triangular pyramid

A triangular pyramid (tetrahedron) has 4 triangular faces.

Step4: Calculate the total area of all faces

Multiply the area of one face by the number of faces:
\( A_{total} = 4 \times 170 = 680 \) square feet.

Answer:

B. 680 sq ft