# GMAT Quant Practice Questions - **Geometry**

You may get five to seven questions from Geometry in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include lines, angles, triangles, quadrilaterals, circles, coordinate geometry and solid geometry. A collection of GMAT practice questions from Geometry is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?

- Square
- Rectangle but not a square
- Rhombus
- Parallelogram but not a rhombus
- Kite

**Correct Answer**Choice (C).

The quadrilateral is a Rhombus. Correct answer- Explanatory Answer
- Quadrilaterals
- Medium

What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150

^{o}?- 24 sq units
- 48 sq units
- Such a triangle does not exist

**Correct Answer**Choice (A).

The area of the obtuse angled triangle is 24 sq units. Correct answer- Explanatory Answer
- Triangle Area
- Easy

What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?

- 6
- 4
- 24.5
- 20.5
- 12.5

**Correct Answer**Choice (D).

The radius of the circumscribing circle is 20.5 units. Correct answer- Explanatory Answer
- Right triangle properties
- Medium

If the sum of the interior angles of a regular polygon measures 1440

^{o}, how many sides does the polygon have?- 10 sides
- 8 sides
- 12 sides
- 9 sides
- None of these

**Correct Answer**Choice (A).

The regular polygon has 10 sides. Correct answer- Explanatory Answer
- Regular Polygons
- Easy

What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

- 2 units
- 12 units
- 6.5 units
- 6 units
- 7.5 units

**Correct Answer**Choice (A).

The radius of the inscribed circle is 2 units. Correct answer- Explanatory Answer
- Right Triangle : Inradius
- Medium

How many diagonals does a 63-sided convex polygon have?

- 3780
- 1890
- 3843
- 3906
- 1953

**Correct Answer**Choice (B).

The 63-sided convex polygon has 1890 diagonals. Correct answer- Explanatory Answer
- Convex Polgons : Properties
- Easy

If 10, 12 and 'x' are sides of an acute angled triangle, how many integer values of 'x' are possible?

- 7
- 12
- 9
- 13
- 11

**Correct Answer**Choice (C).

9 integer values are possible for x. Correct answer- Explanatory Answer
- Properties of triangles
- Medium

Is triangle ABC obtuse angled?

- a
^{2}+ b^{2}> c^{2}. - The center of the circle circumscribing the triangle does not lie inside the triangle.

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked; additional data specific to the problem is needed.

**Correct Answer**Choice (E).

The two statements together are NOT sufficient. Correct answer- Explanatory Answer
- Properties of obtuse triangles
- Hard

- a
Is triangle ABC with sides a, b and c acute angled?

- Triangle with sides a
^{2}, b^{2}, c^{2}has an area of 140 sq cms. - Median AD to side BC is equal to altitude AE to side BC.

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked; additional data specific to the problem is needed.

**Correct Answer**Choice (A).

Statement 1 ALONE sufficient; statement 2 is NOT. Correct answer- Explanatory Answer
- Properties of acute triangles
- Hard

- Triangle with sides a

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