QQuestionMathematics
QuestionMathematics
find surface area of a triangular prism with measurements of 26 yd, 24 yd, 10 yd, 18 yd.
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Answer
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Step 1
\begin{align*}
First, we need to find the lengths of the slant height (l) and the height (h) of the triangular faces. We can use the Pythagorean theorem to find l using the given measurements of 26 yd, 24 yd, and 10 yd: l &= \sqrt{26^2 + 24^2} \ &= \sqrt{676 + 576} \ &= \sqrt{1252} \ &\approx 35.38~\text{yd} \end{align*}
Step 2
\begin{align*}
Now, we can find the height (h) of the triangular face using the given measurement of 10 yd and one of the other two measurements. Let's use 26 yd: h &= \sqrt{26^2 - 10^2} \ &= \sqrt{676 - 100} \ &= \sqrt{576} \ &= 24~\text{yd} \end{align*}
Final Answer
\boxed{S = 804~\text{yd}^2}
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