Question

Trapezoid ABCD is graphed in a coordinate plane.

What is the area of the trapezoid?

10 square units
12 square units
20 square units
24 square units

Answer 1

The answer is 12 square units

Explanation:

Answer 2

The area of ABCD is 12 square units. Option b is correct.

Explanation:

From the given figure it is clear that the vertices of triangle are A(-5,-2), B(-1,2), C(0,-1), D(-2,-3).

The area of ABCD is the sum of area of triangle ABC and ACD.

Area of a triangle is

`A=(1)/(2)|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`

Area of triangle ABC is

`A=(1)/(2)|-5(2+1)-1(-1+2)+0(-2-2)|`

`A=(1)/(2)|-16|`

`A=(16)/(2)`

`A=8`

The area of triangle ABC is 8 square units.

Area of triangle ACD is

`A=(1)/(2)|-5(-1+3)+0(-3+2)-2(-2+1)|`

`A=(1)/(2)|-8|`

`A=(8)/(2)`

`A=4`

The area of triangle ABC is 4 square units.

The are of ABCD is

`Area(ABCD)=Area(ABC)+Area(ACD)`

`Area(ABCD)=8+4=12`

Therefore the area of ABCD is 12 square units. Option b is correct.