Question

1. a company is designing a new logo that consists of a shaded triangle inside of a parallelogram. what fraction of the parallelograms area is shaded? lesson practice 6.1.08 name: date:

Explanation:

Step1: Recall area formulas

Area of a parallelogram $A_{p}=bh$, and area of a triangle $A_{t}=\frac{1}{2}bh$. Assume the base and height of the parallelogram are $b$ and $h$. The base and height of the triangle inside the parallelogram are the same as those of the parallelogram.

Step2: Calculate the ratio of areas

Let the base of the parallelogram be $b$ and height be $h$, so $A_{p}=bh$. The area of the triangle with the same base $b$ and height $h$ is $A_{t}=\frac{1}{2}bh$. The fraction of the parallelogram's area that is shaded (the triangle) is $\frac{A_{t}}{A_{p}}$. Substitute the area - formulas: $\frac{\frac{1}{2}bh}{bh}$. The $bh$ terms cancel out, and we get $\frac{1}{2}$.

Answer:

$\frac{1}{2}$