Question

What is the perimeter of trapezoid ABCD?

Round your answer to the nearest tenth.



A.
4.1 units

B.
20.2 units

C.
16.1 units

D.
8.2 units

Answer 1

I think B but don't take my word!!!

Answer 2

B. 20.2 units.

Explanation:

We have been given an image of a trapezoid on coordinate plane. We are asked to find perimeter of our given trapezoid.

First of all, we will find the length of each side of our trapezoid using distance formula, then we will add lengths of all sides to get the perimeter of trapezoid.

`\text{Distance}=√((x_2-x_1)^2+(y_2-y_1)^2)`

`\text{Distance between points A and B}=√((5-1)^2+(3-2)^2)`

`\text{Distance between points A and B}=√((4)^2+(1)^2)`

`\text{Distance between points A and B}=√(16+1)`

`\text{Distance between points A and B}=√(17)`

`\text{Distance between points B and C}=√((5-5)^2+(3--4)^2)`

`\text{Distance between points B and C}=√((0)^2+(3+4)^2)`

`\text{Distance between points B and C}=√(0+(7)^2)`

`\text{Distance between points B and C}=7`

`\text{Distance between points C and D}=√((5-1)^2+(-4--3)^2)`

`\text{Distance between points C and D}=√((4)^2+(-4+3)^2)`

`\text{Distance between points C and D}=√((4)^2+(-1)^2)`

`\text{Distance between points C and D}=√(16+1)`

`\text{Distance between points C and D}=√(17)`

`\text{Distance between points D and A}=√((1-1)^2+(-3-2)^2)`

`\text{Distance between points D and A}=√((0)^2+(-5)^2)`

`\text{Distance between points D and A}=√(25)=5`

`\text{Perimeter of trapezoid ABCD}=√(17)+7+√(17)+5`

`\text{Perimeter of trapezoid ABCD}=2√(17)+12`

`\text{Perimeter of trapezoid ABCD}=8.24621125}+12`

`\text{Perimeter of trapezoid ABCD}=20.24621125}\approx 20.2`

Therefore, the perimeter of trapezoid ABCD is 20.2 units and option B is the correct choice.