An equilateral triangular pyramid has a slant height of 8.3 inches. The triangular base has a perimeter of 4.8 inches and an area of 1.1 square inches. Find the surface area of the pyramid.
so each side of the base has length 4.8/3 = 1.6
The lateral area is 3 triangles, each with base 1.6 and height 8.3
A = 3 * (1.6*8.3)/2 = ____
Sorry, but an equilateral triangle of perimeter 4.8 has an area of
1.6^2/4 * sqrt(3) = 0.55
so how come yours is double that?
To find the surface area of the pyramid, we need to find the area of the triangular base and the area of the three triangular faces.
First, let's find the area of the triangular base.
We know the perimeter of the triangular base is 4.8 inches. Since the base is equilateral, each side of the triangle has the same length. We can then divide the perimeter by 3, as there are three equal sides.
Perimeter = 4.8 inches
Length of each side = Perimeter/3 = 4.8/3 = 1.6 inches
We also know the area of the triangular base is 1.1 square inches.
Area of triangular base = (side length^2 * sqrt(3))/4
1.1 = (1.6^2 * sqrt(3))/4
1.1 = (2.56 * sqrt(3))/4
1.1 * 4 = 2.56 * sqrt(3)
4.4 = 2.56 * sqrt(3)
sqrt(3) = 4.4 / 2.56
sqrt(3) ≈ 1.71875
Next, let's find the area of each of the triangular faces.
The slant height of the pyramid is given as 8.3 inches. This is the height of each triangular face.
Area of triangular face = (base length * height) / 2 = (1.6 * 8.3) / 2 = 6.64 square inches
Now, we can find the surface area of the pyramid by adding the area of the base and three faces together.
Surface area = Area of base + 3 * Area of faces
Surface area = 1.1 + 3 * 6.64 = 1.1 + 19.92 = 21.02 square inches
Therefore, the surface area of the equilateral triangular pyramid is 21.02 square inches.