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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 the triangular base and the area of the three triangular faces.
The area of the triangular base can be found using the formula for the area of a triangle:
Area of base = (1/2) * base * height
= (1/2) * 4.5 cm * 3.9 cm
= 8.775 cm^2
The area of each triangular face can be found using the formula for the area of a triangle:
Area of face = (1/2) * base * height
= (1/2) * 4.5 cm * 3.5 cm
= 7.875 cm^2
Since there are three triangular faces on a pyramid, the total area of all the faces is 3 times the area of one face:
Total area of faces = 3 * 7.875 cm^2
= 23.625 cm^2
To find the surface area of the pyramid, we need to add the area of the base and the area of the faces:
Surface area = Area of base + Total area of faces
= 8.775 cm^2 + 23.625 cm^2
= 32.4 cm^2
Therefore, the surface area of each pyramid is 32.4 cm^2.