Question

This figure is made up of a rectangle and parallelogram.

What is the area of this figure?



Enter your answer in the box. Do not round any side lengths.

units²

Coordinate plane with axes labeled x and y. A closed figure is formed by a parallelogram and rectangle. The vertices are negative 6 comma negative 1, 2 comma 1, 2 comma 7, 3 comma 3, 3 comma negative 3, and negative 5 comma negative 5.

Answer 1

9514 1404 393

Answer:

40 units²

Explanation:

You can figure the side lengths using the distance formula, or you can use a formula for finding area from coordinates. The latter looks like ...

`\displaystyle A=(1)/(2)\left|\sum\limits_(k=1)^n{x_k(y_(k-1)-y_(k+1))}\right|\qquad\text{where $y_0=y_n$ and $y_(n+1)=y_1$}`

So, the area is ...

A = (1/2)|(-6(-5-1) +2(-1-7) +2(1-3) +3(7+3) +3(3+5) -5(-3+1)|

= (1/2)|36 -16 -4 +30 +24 +10| = (1/2)(80)

A = 40

The area of the figure is 40 units².