Carcass wrote:
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 the quadrilateral region BCDE?
A) 1/2
B) 1/3
C) 1/4
D) 1/5
E) 1/6
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 ADThis means AE = ED
So, let's let AE = ED =
1We get:
ABCD is a parallelogramProperty: Opposite sides in a parallelogram have equal lengths
Since AD = 2, it must also be the case that CB =
2To 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
1Area of triangle = (base)(height)/2
So, the area of ABE = (
1)(
1)/2 =
0.5Area 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 =
1/3Answer: B
Cheers,
Brent