What is the surface area of this triangular pyramid? 3 mm 4 mm 4 mm 4 mm 3.5 mm
To find the surface area of a triangular pyramid, we need to calculate the area of each face and then sum them up.
The triangular pyramid has a triangular base with side lengths of 4 mm, 4 mm, and 3 mm. We can use Heron's formula to find the area of this base. Let's denote the side lengths as a = 4 mm, b = 4 mm, and c = 3 mm.
First, calculate the semiperimeter, s:
s = (a + b + c) / 2
s = (4 + 4 + 3) / 2
s = 11 / 2
s = 5.5 mm
Then, calculate the base area, A:
A = √(s(s-a)(s-b)(s-c))
A = √(5.5(5.5-4)(5.5-4)(5.5-3))
A = √(5.5(1.5)(1.5)(2.5))
A = √(24.375)
A ≈ 4.94 mm²
Therefore, the base area is approximately 4.94 mm².
Next, we need to calculate the areas of the triangular faces. The height of the pyramid is 3.5 mm. We can use the formula for the area of a triangle to find the area of each face:
face area = (1/2) * base length * height
face area = (1/2) * 3 mm * 3.5 mm
face area = 5.25 mm²
Since there are 3 triangular faces, the total surface area of the pyramid is:
Surface area = base area + 3 * face area
Surface area = 4.94 + 3 * 5.25
Surface area = 4.94 + 15.75
Surface area ≈ 20.69 mm²
Therefore, the surface area of this triangular pyramid is approximately 20.69 mm².