To calculate the surface area of a triangular pyramid (also known as a tetrahedron), you need to find the area of the base and the area of the three triangular faces.
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Calculate the area of the triangular base.
The base is a triangle with a base of 5 inches and height of 4.3 inches.
\[ \text{Area of the base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 4.3 = \frac{21.5}{2} = 10.75 \text{ in.}^2 \] -
Calculate the area of the triangular faces.
Each triangular face has a base of 5 inches and a height equal to the slant height of 6 inches. \[ \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 6 = 15 \text{ in.}^2 \] Since there are three triangular faces: \[ \text{Total area of the three triangular faces} = 3 \times 15 = 45 \text{ in.}^2 \] -
Calculate the total surface area.
\[ \text{Surface Area} = \text{Area of the base} + \text{Total area of the triangular faces} = 10.75 + 45 = 55.75 \text{ in.}^2 \]
Therefore, the surface area of the chocolate pyramid is 55.75 in.².
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