Right Rectangular Prisms & Pyramids Unit Test
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Question
Use the image to answer the question.
An illustration shows a 3 D triangular prism. The side of the base is 4.5 centimeters. The perpendicular height of the triangular base is 3.9 centimeters. The perpendicular height of the lateral face from the apex to the center of the base is 3.5 centimeters. There are two right angle symbols to show the perpendicular lines. The heights are shown as dashed lines.
A metalworker is creating decorative points in the form of triangular pyramids to go on top of a fence she is building. She wants to know the surface area of each pyramid. Use the surface area formula to find the surface area of each pyramid based on the figure.
(1 point)
To find the surface area of a triangular pyramid, you need to find the area of the base and the area of each triangular face.
The area of the base can be found using the formula for the area of a triangle, which is 1/2 * base * height. In this case, the base of the pyramid is the side of the triangular base, which is 4.5 cm, and the height of the base is the perpendicular height of the triangular base, which is 3.9 cm. So the area of the base is 1/2 * 4.5 cm * 3.9 cm.
To find the area of each triangular face, you need to know the length of the slant height. The slant height is the perpendicular height of the lateral face from the apex to the center of the base, which is 3.5 cm. The base of the triangular face is the same as the base of the pyramid, which is 4.5 cm. So you can use the formula for the area of a triangle again to find the area of each triangular face, which is 1/2 * base * height. In this case, the height is the slant height, which is 3.5 cm.
To find the total surface area of the pyramid, you add the area of the base to the sum of the areas of the triangular faces.