To find the surface area of the triangular pyramid, we need to calculate the area of the base triangle and the area of the three triangular faces.
First, calculate the area of the base triangle:
Area of an equilateral triangle = (√3 / 4) * side length^2
Area of base triangle = (√3 / 4) * (4.5 cm)^2
Area of base triangle = (√3 / 4) * 20.25 cm^2
Area of base triangle = 4.43 cm^2
Next, calculate the area of each triangular face:
Area of a triangle = (1/2) * base * height
Area of each triangular face = (1/2) * 4.5 cm * 3.5 cm
Area of each triangular face = 7.88 cm^2
Now, calculate the total surface area by adding the area of the base triangle and the three triangular faces:
Total surface area = 4.43 cm^2 + 3 * 7.88 cm^2
Total surface area = 4.43 cm^2 + 23.64 cm^2
Total surface area = 28.07 cm^2
Therefore, the surface area of the triangular pyramid is 28.07 cm^2.
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
1 answer
1 answer