Question

Find (x,y) and the find the area of the trapezoid

Answer 1

(12,13)

Explanation:

(x , y) is vertically above (12 , 5)

So x = 12

18 - y = 5 - 0

18 - y = 5

y = 18 - 5

y = 13

Answer 2

(12, 13)

156 square units

Explanation:

This is an isosceles trapezoid, which means that the endpoints of the smaller base will be the same distance away from the endpoints of the larger base.

Since (12, 5) is 5 units away vertically from (0, 0), then (x, y) should also be 5 units away vertically from (0, 18). So, the y-coordinate of (x, y) should be 18 - 5 = 13. The x-coordinate should remain the same as the x-coordinate from (12, 5) because they lie on the same line.

So, (x, y) is (12, 13).

The area of a trapezoid is:
`A=((b_1+b_2)*h)/(2)`, where b1 and b2 are the bases and h is the height.

Here, the bases are b1 = 18 and b2 = 13 - 5 = 8. The height is 12 - 0 = 12. So:

`A=((b_1+b_2)*h)/(2)`

`A=((18+8)*12)/(2)=156`

The area is 156 units squared.