Question

# Veronica made a triangle by taking an 8 1/2 × 11 sheet of paper and putting a dot at the top. She then drew lines from the bottom corners to the dot a

Right triangles and trigonometry

Veronica made a triangle by taking an 8 $$\frac{1}{2} \times 11$$ sheet of paper and putting a dot at the top. She then drew lines from the bottom corners to the dot and cut along the lines (see diagram).
What is the area of the triangle that Veronica cut out?

Note that an $$\displaystyle{8}{\left(\frac{{1}}{{2}}\right)}×{11}$$ sheet of paper is measured in inches.
The area of a triangle with base b and corresponding height h is given by: $$\displaystyle{A}={\left(\frac{{1}}{{2}}\right)}{b}{h}$$
Substitute $$b=8.5$$ in. and $$h=11$$ in.: $$\displaystyle{A}={\left(\frac{{1}}{{2}}\right)}{\left({8.5}\right)}{\left({11}\right)}$$
$$\displaystyle{A}={46.75}\in^{{2}}$$