A sign company is building a sign with the dimensions shown. $$10 {ft}$$ ![](http://admin.getprephub.com/media/editor/c3_20230225231507951100.png) What is the area, in square feet, of the sign?

Given that, $$A D=C D=\frac{10}{2}=5$$ ![](http://admin.getprephub.com/media/editor/c3s_20230225231518836129.png) In right triangle $$A B D$$, $$B D^{2}+A D^{2}=A B^{2}$$ or, $$B D^{2}=A B^{2}-A D^{2}$$ or, $$B D^{2}=13^{2}-5^{2}=169-25$$ or, $$B D^{2}=144$$ Or, $${BD}=12$$ Area of the sign= area of $$\triangle A B C=\frac{1}{2} \times A C \times B D=\frac{1}{2} \times 10 \times 12=60$$ square feet

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A sign company is building a sign with the dimensions shown.

$10 {ft}$

What is the area, in square feet, of the sign?

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