Surface Area Unit Test
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Question
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
(1 point)
cm2
To find the surface area of the rectangular pyramid, we need to calculate the area of each face and then add them up.
1. The area of the rectangular base is 14 cm * 12 cm = 168 cm^2.
2. The area of each of the four triangular faces can be found by using the formula for the area of a triangle: 0.5 * base * height.
a. For the face with base 14 cm and height 10 cm, the area is 0.5 * 14 cm * 10 cm = 70 cm^2.
b. For the face with base 12 cm and height 10.6 cm, the area is 0.5 * 12 cm * 10.6 cm = 63.6 cm^2.
3. Add up the areas of all faces: 168 cm^2 (base) + 70 cm^2 + 70 cm^2 + 63.6 cm^2 + 63.6 cm^2 = 335.2 cm^2.
Therefore, the surface area of the rectangular pyramid is 335.2 cm^2.