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
