Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Identify the dimensions of the triangular base

Using the Pythagorean Theorem knowledge point

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Calculate the area of the two triangular bases

The two bases are congruent right triangles with legs of \(15\text{ yd}\) and \(20\text{ yd}\).

$$ A_{\text{base}} = \frac{1}{2} \times 15 \times 20 = 150\text{ yd}^2 $$

$$ A_{\text{both bases}} = 2 \times 150 = 300\text{ yd}^2 $$

Calculate the lateral surface area of the prism

The prism has a height (length) of \(h = 19\text{ yd}\).
The perimeter of the triangular base is:

$$ P = 15 + 20 + 25 = 60\text{ yd} $$

The lateral area is:

$$ A_{\text{lateral}} = P \times h = 60 \times 19 = 1140\text{ yd}^2 $$

Calculate the total surface area

The total surface area is the sum of the lateral area and the area of the two bases.

$$ A_{\text{total}} = A_{\text{lateral}} + A_{\text{both bases}} = 1140 + 300 = 1440\text{ yd}^2 $$

Answer:

Find the surface area of this triangular prism. Be sure to include the correct unit in your answer. <blank>\(1440\text{ yd}^2\)</blank>