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Find the surface area of the regular pyramid to the nearest hundredth.

Find the surface area of the regular pyramid to the nearest hundredth.

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Find trigonometric functions using a calculator

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Q. Find the surface area of the regular pyramid to the nearest hundredth.

Base Area Calculation: First, we need to know the base area and slant height of the pyramid to calculate its surface area. Let's assume the base is a square with side length $10\,\text{cm}$ and the slant height is $15\,\text{cm}$ .
Calculate Base Area: Calculate the area of the base. The formula for the area of a square is side length squared. $\newline$ Area of base = side length $\times$ side length = $10\, \text{cm} \times 10\, \text{cm} = 100\, \text{cm}^2$ .
Calculate Lateral Surface Area: Next, calculate the lateral surface area. The formula for the lateral surface area of a regular pyramid is $(\text{perimeter of base} \times \text{slant height}) / 2$ . $\newline$ Perimeter of base = $4 \times \text{side length} = 4 \times 10 \, \text{cm} = 40 \, \text{cm}$ . $\newline$ Lateral surface area = $(40 \, \text{cm} \times 15 \, \text{cm}) / 2 = 300 \, \text{cm}^2$ .
Find Total Surface Area: Add the base area and the lateral surface area to find the total surface area. $\newline$ Total surface area = base area + lateral surface area = $100 \, \text{cm}^2 + 300 \, \text{cm}^2 = 400 \, \text{cm}^2$ .

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