Question

Select the correct answer. What is the approximate perimeter of trapezoid DEFG? Round your answer to the nearest hundredth. A. 12 units B. 12.04 units C. 12.48 units D. 13 units

Answer 1

C. 12.48 units

Explanation:

Perimeter of the trapezoid = DE + EF + FG + GD

DE = |-2 - 1| = 3 units

FG = |-3 - 2| = 5 units

Find EF and GD using distance formula

✔️Distance between E(1, 3) and F(2, 1):

`EF = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

(x1, y1) = (1, 3)

(x2, y2) = (2, 1)

Substitute

`EF = √((2 - 1)^2 + (1 - 3)^2)`

`EF = √((1)^2 + (-2)^2)`

`EF = √(1 + 4)`

`EF = √(5)`

`EF = 2.24 units`

✔️Distance between G(-3, 1) and D(-2, 3):

`GD = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

(x1, y1) = (-3, 1)

(x2, y2) = (-2, 3)

Substitute

`GD = √((-2 -(-3))^2 + (3 - 1)^2)`

`GD = √((-1)^2 + (2)^2)`

`GD = √(1 + 4)`

`GD = √(5)`

`GD = 2.24 units`

✅Perimeter = 3 + 2.24 + 5 + 2.24 = 12.48 units