Question

On a coordinate plane, trapezoid A B C D has points (10, 6), (4, 10), (14, 16), (16, 10). What is the area of the trapezoid? 30 square units 60 square units 90 square units 120 square units

Answer 1

Answer:

  60 square units

Step-by-step explanation:

When given only a list of coordinates, it can sometimes be convenient to compute the area from the sum ...

  $A=\dfrac{1}{2}\left|\sum\limits_{k=1}^n{(y_{k+1}-y_{k-1})x_k}\right|$

where the indices of the points "wrap around". Here, we are given the points ...

  (10, 6), (4, 10), (14, 16), (16, 10)

so this computation gives ...

  A = (1/2)|10(10-10) +4(16-6) +14(10-10) +16(6-16)|

  = (1/2)|0 +40 +0 -160| = (1/2)(120)

  A = 60

The area of the trapezoid is 60 square units.