# GMAT Geometry Questions With Answers

Geometry questions constitute a major portion of the Quant section of the GMAT. These questions can come under both Problem Solving and Data Sufficiency types.Geometry has a number of topics in it. In this article, we will be looking into –

1. GMAT Geometry Topics
2. GMAT Geometry Questions with Answers

## GMAT Geometry Topics

In the GMAT, Geometry constitutes a number of topics. They are as follows (this list is in accordance with the GMAT Official Guide):

1. Lines and Angles
2. Convex Polygons
3. Triangles
5. Circles
6. Rectangular solids and cylinders
7. Coordinate Geometry

## Examples – GMAT Geometry Questions with Answers and explanations

### Question 1:

If a convex polygon has 5 diagonals, what is the sum of internal angles of the polygon?

### Approach:

The number of diagonals is equal to the total number of lines formed by joining any two vertices minus the number of sides.

Hence, the number of diagonals = nC2 – n = n(n-1)/2 – n = n(n-3)/2 = 5

n(n-3) = 10

n = 5

Hence, the sum of internal angles = (5-2) x 180 = 540 degrees.

### Question 2:

The length of the equal sides of an isosceles triangle is 6 cm. What is the maximum possible area of the triangle(in square centimetres)?

### Approach:

Let us assume that one of these 6 cm sides is the base and the angle that the other 6 cm side makes with the base is k degrees.

Now, we know that the area of a triangle whose 2 adjacent sides are known and the enclosed angle is known can be calculated as:

Area = (1/2)*a*b*sin(k)

a = First side

b = Second side

k is the angle enclosed.

Now, a and b are fixed as 6 cm each

If sin k is maximum = 1, the value will be maximum.

Hence, the maximum possible area = (1/2) x 6 x 6 = 18

### Question 3:

What is the radius of a circle C?

Statement 1: The ratio of the circumference and the diameter = 3.14

Statement 2: The ratio of the area and the circumference is 5.4 units.

Approach:

Statement 1: Circumference = 2 * pi * r

Diameter = 2 * r

Ratio = pi

The statement does not add any value to the information that is provided.

Statement 2: The ratio of the area and the circumference is 5.4 units.

pi * r * r / (2 * pi * r) = 5.4

r = 10.8 units.

Hence, Option B – Statement 1 alone is not sufficient, Statement 2 alone is sufficient is the correct choice.

### Note:

Though these examples provide a good sense of what type of GMAT Geometry questions you can expect, in no way do they represent the exhaustive list of concepts required for the Quantitative section of GMAT.

### Tips to keep in mind:

1. Try to take some time out from the Problem-Solving Geometry questions so that you can use that time to solve the tricky Data Sufficiency Geometry questions.
2. Do not get stuck in a question for long. If you find yourself trapped in a question for long, take a guess and move on.
3. Read the units(if any) carefully.
4. Look out for negation words. For example: Which of the following are NOT possible values of x?
5. Some questions can be solved faster by the use of options. Make sure you don’t solve these questions in a conventional way.

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