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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
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Answer 1

To find the surface area of the rectangular pyramid, we need to calculate the area of each face and then add them all together.

First, let's find the area of the base. The formula for the area of a rectangle is length x width, so the area of the base is 14 cm x 12 cm = 168 cm².

Next, we need to find the areas of the four triangular faces. Since the pyramid is rectangular, the four triangular faces are all congruent. The formula for the area of a triangle is 0.5 x base x height.

For the two faces with base length 14 cm, the area is 0.5 x 14 cm x 10 cm = 70 cm².
For the two faces with base width 12 cm, the area is 0.5 x 12 cm x 10.6 cm = 63.6 cm².

Now, we can find the total surface area by adding up the areas of the base and the four triangular faces:

168 cm² (base) + 70 cm² + 70 cm² + 63.6 cm² + 63.6 cm² = 435.2 cm²

Therefore, the surface area of the rectangular pyramid is 435.2 cm².