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 a pyramid, we use the formula:
Surface Area = Base Area + (1/2) * Perimeter * Slant Height.
First, we need to find the base area of the pyramid. The base of the pyramid is a triangle, so we can use the formula for the area of a triangle, which is:
Base Area = (1/2) * base * height.
In this case, the base of the pyramid is the triangular base of the prism, which has a height of 3.9 cm and a base length of 4.5 cm. So the base area is:
Base Area = (1/2) * 4.5 cm * 3.9 cm = 8.775 cm^2.
Next, we need to find the slant height of the pyramid. The slant height is the distance from the apex (top point) of the pyramid to the center of the base. In this case, the slant height is given as 3.5 cm.
Lastly, we need to find the perimeter of the base. The base of the pyramid is a triangle, so we can find the perimeter by adding up the lengths of all three sides. In this case, we know the base length is 4.5 cm, but we don't have enough information to find the lengths of the other two sides. Therefore, we cannot calculate the perimeter at this time.
Since we don't have enough information to calculate the perimeter, we cannot calculate the surface area of the pyramid.