Question

Why is the answer D for question #49?

Answer 1

The formula for the area if a trapezium is
$\frac{a + b}{2} h$
A and B are the parallel widths of the trapezium and h is the height of the trapezium. In this case a=AB, b=DC and h=AE.
We are told that AE is 10 units long, so h=10.
We are also told that DC is 28 units long, so b=28.
We now need to figure out the value of a (length AB). The information says that the area of triangle EBA is 60 square units (and we can see that its perpendicular sides are AE and AB). So, we can work backwards to find out length AB.
For the given area, you would normally do:
(10×AB)÷2=60
Now working backwards:
1) Multiply by 2 on both sides - 10×AB=120
2) Divide by 10 on both sides - AB=12
This means that our final value (a) for the trapezium formula is 12. Now, we just substitute the values:
$\frac{(12 + 28)}{2} \times 10 \\ \frac{40}{2} \times 10 \\ 20 \times 10 \\ = 200$
So, the area of the trapezium is 200 square units.

Answer 2

Area of EBA = 60
(10 * AB)/2 = 60
AB = 12
Trapezoid Area = (12 + 28) /2 * height
Trapezoid Area = 20 *10
Trapezoid Area = 200 which is D