Use the image to answer the question.
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?
(1 point)
mm2
To find the surface area of the rectangular pyramid, we need to calculate the area of the individual faces and then sum them up.
The rectangular base has dimensions of 8mm by 10mm, so the area of the base is 8mm * 10mm = 80mm^2.
Now, we need to calculate the areas of the 4 triangles on the lateral faces.
Since the perpendicular height from the apex to the base length is 12mm, the area of one of the triangles with base length 8mm is 0.5 * 8mm * 12mm = 48mm^2.
Similarly, since the perpendicular height from the apex to the base width is 15mm, the area of one of the triangles with base width 10mm is 0.5 * 10mm * 15mm = 75mm^2.
There are 4 of these triangles, so the total area of the 4 triangles is 4 * (48mm^2 + 75mm^2) = 492mm^2.
Adding the area of the base and the lateral faces, the total surface area of the rectangular pyramid is 80mm^2 + 492mm^2 = 572mm^2.
Therefore, the surface area of the rectangular pyramid is 572 mm^2.