To find the surface area of a triangular pyramid, we need to find the area of each triangular face and the area of the base, and then sum them all up.
1. Area of the base:
The base of the pyramid is a triangle with a base of 5 inches and a height of 4.3 inches. The formula to find the area of a triangle is:
Area = (base * height) / 2
Area of the base = (5 * 4.3) / 2 = 10.75 square inches.
2. Area of each triangular face:
The triangular face of the pyramid is an isosceles triangle, with two sides of 6 inches and a base of 5 inches. To find the area of the triangular face, we can use Heron's formula:
Area = sqrt(s * (s - a) * (s - b) * (s - c)), where s is the semi-perimeter of the triangle and a, b, c are the lengths of its sides.
In this case, a = b = 6 inches and c = 5 inches.
s = (a + b + c) / 2 = (6 + 6 + 5) / 2 = 8.5 inches (semi-perimeter)
Area of each triangular face = sqrt(8.5 * (8.5 - 6) * (8.5 - 6) * (8.5 - 5)) = 12.688 square inches (rounded to three decimal places).
3. Total surface area:
The pyramid has 4 triangular faces and 1 base.
Total surface area = 4 * Area of each triangular face + Area of the base
Total surface area = 4 * 12.688 + 10.75 = 50.752 + 10.75 = 61.502 square inches (rounded to three decimal places).
Therefore, the surface area of the chocolate pyramid is approximately 61.502 square inches.
A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid the pyramid has a base of 5 in and a height of 4.3 in and a slant of 6 in use the correct formula to find the surface area of the chocolate pyramid
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