What is the area of the triangle ABC?

This topic has expert replies
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

What is the area of the triangle ABC?

by Vincen » Mon Jan 29, 2018 3:07 am
What is the area of the triangle ABC?

(1) The edge AB of the triangle is 8 inches.

(2) Triangle ABC is equilateral

The OA is C.

How can I find the area just knowing that the triangle is equilateral? Experts, can you help me? I'd appreciate your help here.

GMAT/MBA Expert

User avatar
Legendary Member
Posts: 503
Joined: Thu Jul 20, 2017 9:03 am
Thanked: 86 times
Followed by:15 members
GMAT Score:770

by ErikaPrepScholar » Tue Jan 30, 2018 6:12 am
We can work through this problem really quickly if we happen to know that we can solve for the area of an equilateral triangle using:
$$A=\frac{\sqrt{3}}{4}a^2$$
where a is the length of one side of the triangle.

However, even if we don't know that, we can still solve. We know that all sides of the triangle are 8 inches long because the triangle is equilateral. envision dividing our equilateral triangle in half, giving two right triangles with a base of 4 and a hypotenuse of 8. Using the pythagorean theorem, we can then solve for the height by plugging in
$$4^2+h^2=8^2$$
$$h^2=80$$
$$h=4\sqrt{5}$$
Once we fing the height, we can then solve for the area of the equilateral triangle using
$$A=\frac{1}{2}bh$$
where b = 8:
$$A=\frac{1}{2}8*4\sqrt{5}$$
$$A=16\sqrt{5}$$
So the statements are sufficient together. Of course, we don't actually need to solve for the area, or even the height of the triangle - since this is DS, all we need to do is know that if we know the length of one side on an equilateral triangle, we can find the area and solve the problem.
Image

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog