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)
cm2
To find the surface area of the triangular pyramid, we need to calculate the area of its base and the area of its lateral faces.
The base of the pyramid is a triangle, and we know that the length of one side of the base is 4.5 centimeters and the perpendicular height of the triangular base is 3.9 centimeters. To find the area of the base triangle, we can use the formula for the area of a triangle, which is (base x height) / 2. So, the area of the base triangle is (4.5 cm x 3.9 cm) / 2 = 17.55 cm^2.
The lateral faces of the pyramid are three congruent triangles that slant upward from the base to the apex. The perpendicular height of each lateral face from the apex to the center of the base is given as 3.5 centimeters. To find the area of each lateral face, we can again use the formula for the area of a triangle. So, the area of each lateral face is (3.5 cm x 4.5 cm) / 2 = 15.75 cm^2.
Since there are three identical lateral faces, the total area of the lateral faces is 3 x 15.75 cm^2 = 47.25 cm^2.
To find the total surface area of the pyramid, we need to add the area of the base triangle to the total area of the lateral faces. So, the surface area of the pyramid is 17.55 cm^2 + 47.25 cm^2 = 64.8 cm^2.
Therefore, the surface area of each pyramid is 64.8 square centimeters.