GMAT Quant: Geometry – Quadrilaterals

In GMAT exam, Geometry questions are the most scoring one. Few basic concepts and formulas can help you solve geometry questions in faction of seconds. Here are few Geometry Sample Questions for GMAT Exam. Let’s learn all about Quadrilaterals.

What is a Quadrilateral?

Any figure that has four sides can be termed as a quadrilateral. There can be many forms of quadrilateral, such as, rhombus, square, rectangle, trapezium, parallelogram etc.

Types of quadrilateral and their properties:

1. Square

• All sides are equal and spread at an angle of 90^o. While, its opposite sides are parallel to one another.
• The diagonals of a square are equal and bisect one another at an angle of 90 

2. Rectangle

• The opposite sides of a rectangle are parallel and equal.
• All sides are spread at an angle of 90^o
• The diagonals are equal in length.
• The diagonals of a rectangle bisect each other at 90^o.
• A rectangle is a special type of parallelogram whose all sides are spread at an angle of 90^o.

3. Parallelogram

• The diagonals of a parallelogram bisect one another.
• Opposite sides of a parallelogram are equal and parallel.
• In a parallelogram, opposite angles are equal.
• The sum of adjacent angle is equal to 180^o.

4. Rhombus

• All sides of a rhombus are equal.
• Only the opposite angles are equal.
• The sum of adjacent angles is supplementary
• The diagonals bisect one another at complementary angle.

5. Kite

• The adjacent sides of a kite are equal in length
• The diagonals bisect one another at complementary angle.
• OX = OY (Where O is the point of intersection)

6. Trapezoid

• Trapezoid is a four sided figure which has only one pair of parallel sides
• The sum of adjacent sides is equal to 180^o.

The most favorite quadrilateral figure of GMAT is parallelogram.

So, what exactly is a parallelogram?

A parallelogram is a four sided figure whose opposite sides are equal and parallel to one another and only the opposite angles are equal.

Let’s solve some questions to see how GMAT plans on confusing its aspirants.

Question: Calculate the area of the parallelogram:

Solution: Area \; of \; parallelogram \; = \; base \times height

Here, height = 8 cm and base = 23 cm

So, Area = \; 8 \times 23 = 184 \; cm^{2}

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