Use Nets for Triangular Pyramids Practice
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Question
Use the image to answer the question.
An illustration shows a triangular pyramid. The perpendicular height of the base measures 3.9 centimeters and its sides measure 4.5 centimeters. The slant height measures 3.5 centimeters.
Find the surface area of the solid figure with an equilateral triangle base.
(1 point)
cm2
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To find the surface area of the triangular pyramid, we first need to calculate the area of the base triangle. Since it is an equilateral triangle, we can use the formula for the area of an equilateral triangle:
Area = (sqrt(3) / 4) * side^2
Area = (sqrt(3) / 4) * 4.5^2
Area = (sqrt(3) / 4) * 20.25
Area = (1.732 / 4) * 20.25
Area = 4.32 * 20.25
Area = 87.48 cm^2
Next, we need to calculate the area of the three triangular faces. Each face is a right triangle with base 4.5 cm, height 3.9 cm, and slant height 3.5 cm. We can use the formula for the area of a triangle:
Area = 0.5 * base * height
Area = 0.5 * 4.5 * 3.9
Area = 0.5 * 17.55
Area = 8.775 cm^2
Since there are three identical faces, the total area of the three faces is:
Total area = 3 * 8.775
Total area = 26.325 cm^2
Finally, we can calculate the total surface area of the triangular pyramid by adding the area of the base and the area of the three faces:
Total surface area = base area + total area of faces
Total surface area = 87.48 + 26.325
Total surface area = 113.805 cm^2
Therefore, the surface area of the triangular pyramid is 113.805 cm^2.