Surface Area of Rectangular Pyramids Practice

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An illustration shows a pyramid with a rectangular base. The length of the base is 8 millimeters and the width 10 millimeters. The perpendicular heights from the apex to the base length is 12 millimeters and to the base width is 15 millimeters. 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?

Answer 1

To find the surface area of the rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.

First, calculate the area of the base:
Area of the base = length * width
Area of the base = 8 mm * 10 mm
Area of the base = 80 mm^2

Next, calculate the area of the four triangular faces:
Area of each triangular face = 1/2 * base * height
Area of each triangular face from apex to length = 1/2 * 8 mm * 12 mm = 48 mm^2
Area of each triangular face from apex to width = 1/2 * 10 mm * 15 mm = 75 mm^2

Now, add up the areas of the base and the four triangular faces:
Surface area = 80 mm^2 + 48 mm^2 + 48 mm^2 + 75 mm^2 + 75 mm^2
Surface area = 326 mm^2

Therefore, the surface area of the rectangular pyramid is 326 square millimeters.