Question

A parallelogram has angles of measure $45$ degrees and $135$ degrees. The shorter side of the parallelogram measure $2.83$ meters, and the other side is $8.83$ meters. Calculate the approximate area of the parallelogram.

• A. $8.83m^2$
• B. $12.49m^2$
• C. $17.67m^2$
• D. $23.32m^2$
• E. $24.99m^2$

Answer 1

The correct option is C $17.67m^2$

The parallelogram can be divided into two triangles and a rectangle

Here angles between adjacent sides are $45$ degrees and $135$ degrees

So the two triangles are isosceles right angled triangle with area $\frac{(2.83{)}^2}{4}$

So the area of two triangles combined is $\frac{(2.83{)}^2}{2}=4.0044$

The area of rectangle is $\frac{2.83}{\sqrt{2}}(8.83-\frac{2.83}{\sqrt{2}})=13.6654$

therefore the area of parallelogram is $4.0044+13.6654=17.67$