To find the surface area of a triangular pyramid, we need to calculate the area of the base and the area of the three triangular faces.
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Area of the Base: The base of the pyramid is a triangle. The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Here, the base of the triangle is 5 inches, and the height is 4.3 inches. So, \[ A_{\text{base}} = \frac{1}{2} \times 5 \times 4.3 = \frac{21.5}{2} = 10.75 , \text{in}^2 \]
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Area of the Three Triangular Faces: Each triangular face has a base of 5 inches (the same as the base of the pyramid), and a slant height of 6 inches. The area of each triangular face is given by: \[ A_{\text{face}} = \frac{1}{2} \times \text{base} \times \text{height} \] Using the slant height as the height: \[ A_{\text{face}} = \frac{1}{2} \times 5 \times 6 = \frac{30}{2} = 15 , \text{in}^2 \] Since there are three triangular faces, the total area of the triangular faces is: \[ A_{\text{triangles}} = 3 \times 15 = 45 , \text{in}^2 \]
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Total Surface Area: Now we can find the total surface area \( A_{\text{total}} \) of the pyramid: \[ A_{\text{total}} = A_{\text{base}} + A_{\text{triangles}} = 10.75 + 45 = 55.75 , \text{in}^2 \]
Thus, the surface area of the chocolate pyramid is 55.75 in.².
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