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
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To find the surface area of the rectangular pyramid, we need to calculate the area of the base and the total area of the four triangular faces.
1. Area of the base:
Area = length x width
Area = 14 cm x 12 cm = 168 cm²
2. Area of the four triangular faces:
We need to calculate the area of each triangular face and then add them together.
a. Front face:
Area = 1/2 x base x height
Area = 1/2 x 14 cm x 10 cm = 70 cm²
b. Back face:
Area = 1/2 x base x height
Area = 1/2 x 14 cm x 10 cm = 70 cm²
c. Left face:
Area = 1/2 x base x height
Area = 1/2 x 12 cm x 10.6 cm ≈ 63.6 cm²
d. Right face:
Area = 1/2 x base x height
Area = 1/2 x 12 cm x 10.6 cm ≈ 63.6 cm²
3. Total surface area:
Total surface area = Area of the base + Area of the four triangular faces
Total surface area = 168 cm² + 70 cm² + 70 cm² + 63.6 cm² + 63.6 cm²
Total surface area = 435.2 cm²
Therefore, the surface area of the rectangular pyramid is 435.2 cm².