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, let's find the area of the base triangle. Since the base is an equilateral triangle, we can use the formula for the area of an equilateral triangle:
Area of base triangle = (sqrt(3) / 4) x side^2
Area of base triangle = (sqrt(3) / 4) x 4.5^2
Area of base triangle = (sqrt(3) / 4) x 20.25
Area of base triangle ≈ 9.35 cm^2
Next, let's find the area of the three triangular faces. Each face is a triangle with base the side of the base triangle and height the slant height of the pyramid.
Area of triangular face = (1/2) x base x height
Area of triangular face = (1/2) x 4.5 x 3.5
Area of triangular face ≈ 7.88 cm^2
Now, the total surface area of the pyramid is the sum of the areas of the base triangle and the three triangular faces:
Total surface area = Area of base triangle + 3 x Area of triangular face
Total surface area ≈ 9.35 + 3(7.88)
Total surface area ≈ 33.99 cm^2
Therefore, the surface area of the triangular pyramid is approximately 33.99 square centimeters.
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 answer