Problem Solving

AbeNeedsAnswers wrote: ↑

Fri Jun 05, 2020 6:11 pm

OG2021PS259.png

In the figure above, ABCD is a parallelogram and E is the midpoint of side AD. The area of triangular region ABE is what fraction of the area of quadrilateral region BCDE?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6

B

Since we're asked to find a certain fraction, we can assign some nice values to the diagram (values that satisfy the given information!)

E is the midpoint of side AD
This means AE = ED
So, let's let AE = ED = 1
We get:


ABCD is a parallelogram
Property: Opposite sides in a parallelogram have equal lengths
Since AD = 2, it must also be the case that CB = 2



To find the areas of triangle ABE and trapezoid BCDE, we need the height of both shapes.
So, let's say the height of both shapes is 1



Area of triangle = (base)(height)/2

So, the area of ABE = (1)(1)/2 = 0.5


Area of trapezoid = (base1 + base2)(height)/2

So, the area of trapezoid BCDE = (1 + 2)(1)/2 = 3/2 = 1.5



The area of triangular region ABE is what fraction of the area of the quadrilateral region BCDE?
(area of triangular region ABE)/(area of the quadrilateral region BCDE) = 0.5/1.5 = 1/3

Answer: B

Cheers,
Brent