Solved Questions on Quadrilateral
Here are some solved examples on quadrilaterals for your help.
Question 1: The perimeter of quadrilateral ABCD is 46 units. AB = x + 7, BC = 2x + 3, CD = 3x – 8, and DA = 4x – 6. Find the length of the shortest side of the quadrilateral.
Solution:
Perimeter = Sum of all sides
= 46 = 10x – 4 or [x = 5]
That gives, AB = 12 units, BC = 13 units, CD = 7 units, DC = 14 units
Hence, length of shortest side is 7 units (i.e. CD).
Question 2: Given a trapezoid ABCD (AB || DC) with median EF. AB = 3x – 5, CD = 2x -1 and EF = 2x + 1. Find the value of EF.
Solution:
We know that the Median of the trapezoid is half the sum of its bases.
= EF = (AB + CD) / 2
= 4x + 2 = 5x – 6 or [x = 8]
Therefore EF = 2x + 1 = 2(8) + 1 => EF = 17 units.
Question 3: In a Parallelogram, adjacent angles are in the ratio of 1:2. Find the measures of all angles of this Parallelogram.
Solution:
Let the adjacent angle be x and 2x.
We know that in of a Parallelogram adjacent angles are supplementary.
= x + 2x = 180° or [x = 60°]
Also, opposite angles are equal in a Parallelogram.
Therefore measures of each angles are 60°, 120°, 60°, 120°.
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Quadrilateral – Definition, Properties, Types, Formulas, Examples
Quadrilateral: A quadrilateral is a two-dimensional figure characterized by having four sides, four vertices, and four angles. It can be broadly classified into two categories: concave and convex. Within the convex category, there are several specific types of quadrilaterals, including trapezoids, parallelograms, rectangles, rhombi, and squares.
The sum of the interior angles of a Quadrilateral is 360°. Let’s learn what is a quadrilateral, its shapes, types, properties, formulas, and examples in detail.
Table of Content
- What is a Quadrilateral?
- Quadrilateral Definition
- Properties of Quadrilateral
- Types of Quadrilateral
- Concave Quadrilateral
- Convex Quadrilateral
- Equilateral Quadrilateral vs Irregular Quadrilaterals
- Quadrilateral Shape
- Trapezium
- Kite
- Parallelogram
- Rectangle
- Rhombus
- Square
- Quadrilateral Theorems
- Quadrilateral Lines of Symmetry
- Quadrilateral Sides and Angles
- Quadrilateral Formulas
- Area of Quadrilateral
- Perimeter of Quadrilateral
- Difference between Different Quadrilaterals
- Solved Questions on Quadrilateral