Question 1 of Timed Quant Practice - Medium Section 2 Sample Test #3

[user7658]

Since it is a trapezoid lines AB and DC have to be parallel to each other (AD and BC clearly are not).

Since AB || DC then angle ADB = angle CBD and angle ABD = angle CDB (Alternate angles).

This means triangle ABD is congruent to CBD because of ASA (The 2 angles and one shared side DB). This means the area of the 2 triangles have to be equal. Area of trapezoid == 11 so area of the 2 triangles == 1/2 == 5.5.

But the correct answer is A.

[Kweku]

@user7658

Since it is a trapezoid lines AB and DC have to be parallel to each other (AD and BC clearly are not).

True

@user7658

Then angle ADB = angle CBD

No. We don’t know that. You said it yourself, AD and BC are not parallel so we can’t alternate-angle them.

@user7658

angle ABD = angle CDB (Alternate angles).

True.

@user7658

This means the area of the 2 triangles have to be equal

No.

Approach it this way:

1. Find the height of the trapezoid as \frac{\text{(6 + 5)}}{\text{2}}×h=11
2. This height is perpendicular to both bases, AB and DC.
3. That means triangle ABD area is \frac{\text{5}}{\text{2}}×2 = 5
4. That means triangle BDC is \frac{\text{6}}{\text{2}}×2 = 6

Qa = 6

[user7658]

ohhhh i see Thanks for pointing that out