|
Quadrilaterals Practice Questions: Quadrilaterals are the most common geometrical shapes we observe in our daily lives. In geometry, a quadrilateral is formed by connecting four points and the points are non-co-linear. These questions on quadrilaterals are designed to make learning about quadrilaterals fun and easy.
In this article, we will discuss quadrilateral and various solved and unsolved practice questions, and concepts, which will help the students increase their scores and improve their problem-solving efficiency. We’ll explore important formulas and tackle a variety of quadrilateral questions with answers, enhancing your ability to solve problems effectively.
What is Quadrilateral?
A Quadrilateral is a Polygon that consists of four sides, four angles, two diagonals and four vertices.
A quadrilateral is a two-dimensional polygon, formed by connecting four points, which are non-co-linear. The angles are located at the four corners or vertices of the quadrilateral. The sum of the total four interior angles of a quadrilateral is 360° and the sum of exterior angles is also 360°.
Formulas of Quadrilaterals
The formulas for different types of quadrilaterals are given below:
|
Quadrilaterals
|
Area
|
Perimeter
|
Diagonal
|
|
Square
|
A = side × side = a2
|
P = 4a
|
D = a√2
|
|
Rectangle
|
A = length (l) × breadth (w)
|
P = 2(l + b)
|
D = √(l2 + b2)
|
|
Trapezium
|
A = 1/2 × (a + b) × h ,
a & b are the lengths of the parallel sides and h is the height.
|
P = a + b + c + d
c & d are the lengths of the non parallel sides
|
|
|
Parallelogram
|
A = b × h
b is the base and h is height
|
P = 2 ×( a+ b)
a & b are the lengths of the adjacent sides
|
|
|
Rhombus
|
A = 1/2 × d1 × d2 ,
(d1, d2 are diagonals)
|
P = 4s
|
Bisect each other at right angles
|
|
Kite
|
A = 1/2 × d1 × d2 ,
(d1, d2 are diagonals)
|
P = 2( a + b),
a & b are the lengths of the adjacent sides
|
|
Quadrilaterals Practice Questions: Solved Examples
1. A rectangle has a length of 12cm and width of 5cm. What is the area of the rectangle?
We know the area of a rectangle = Width × length
then,
Area of the given rectangle = 12 × 5 = 60cm2
2. Each side of a rhombus is 9cm. What is the perimeter of the rhombus?
The formula for the perimeter(P) of a rhombus is,
R = 4 × side length
R = 4×9 = 36cm
3. Find the base of a parallelogram, if its area is 100 cm2 and the height is 5cm.
Here, area = 100 cm2
height = 5cm
We know that the area of a parallelogram = base × height
Base = 100/5
= 20cm
4. Find out the perimeter of a quadrilateral, if its sides are 10, 15, 9, and 4cm.
We know that,
the perimeter of a quadrilateral = sum of all the 4 sides
∴ P = 10+15+9+4 = 38cm
5. Three angles of a quadrilateral are 60°, 85°, 101°. Find out the fourth angle.
We know that the sum of all the four angles of a quadrilateral = 360°
Let the unknown angle be x
Then, 60°+ 85°+ 101°+ x = 360°
246° + x = 360°
x = 114°
6. The diagonals of a kite are 20cm and 12cm, find the area.
We know that,
The area (A) of a kite = 1/2 × diagonal1 × diagonal2
A = 1/2 × 20 × 12
A = 10×12
A = 120 cm2
7. The angles of a quadrilateral are in the ratio of 1:2:3:4. Find the measure of each angle.
The given angles ratio = 1:2:3:4
Let the angles are 1x, 2x, 3x and 4x
We also know that,
the sum of the four angles = 360°
1x + 2x + 3x + 4x = 360°
10x = 360°
x = 36°
Now, putting the value of x, we get the angles
1 × 36° = 36°
2 × 36° = 72°
3 × 36° = 108°
4 × 36° = 144°
8. The lengths of the adjacent sides of a parallelogram are 6cm and 7cm. Find its perimeter.
The adjacent sides of a parallelogram are 6cm and 7cm. That is the base = 6cm and side = 7cm.
Perimeter or P = 2 × (6+7)
P = 2 × 13
∴P = 26 cm.
9. What is the area of a rectangle, having width of 30 mt. and length of 50mt. ?
The area(A) of a rectangle = width × length
A = 30×50
A = 1500 m2 .
10. In a kite, the lengths of the diagonals are 14 cm and 48 cm. One of the angles between the diagonals is 120 degrees. Find the area of the kite.
The area of the kite can be calculated using the formula involving the diagonals:
Area = 1/2 × d1 × d2 × sin(θ)
Here, d1 = 14, d2 = 48, and θ=120∘
Area = 1/2 × 14 × 48 × sin(120∘)
Since sin(120∘) = sin(180∘−60∘) = sin(60∘) = √3/2
Area = 1/2 × 14 × 48 × √3/2
Area = 7 × 48 × √3/2
Area=168√3 cm2
11. In a quadrilateral ABCD, the measures of the angles are ∠A = 4x, ∠B = 3x+10∘, ∠C = 2x, and ∠D = x+20∘. Find the value of x and the measure of each angle.
The sum of the interior angles of a quadrilateral is 360∘.
Given:
∠A + ∠B + ∠C + ∠D = 360∘
Substitute the given angles:
4x + (3x+10∘) + 2x + (x+20∘) = 360∘
Combine like terms:
4x + 3x + 2x + x + 10∘ + 20∘ = 360∘
10x + 30∘= 360∘
Solve for x:
10x = 330∘
x = 33∘
Now, find the measure of each angle:
∠A = 4x = 4 × 33∘= 132∘
∠B = 3x + 10∘= 3 × 33∘+10∘ = 99∘ + 10∘ = 109∘
∠C = 2x = 2 × 33∘= 66∘
∠D = x + 20∘ = 33∘ + 20∘ = 53∘
So, the measures of the angles are:
- ∠A=132∘
- ∠B=109∘
- ∠C=66∘
- ∠D=53∘
Read More,
Quadrilaterals Practice Questions: Unsolved
Frequently Asked Questions on Quadrilaterals- FAQs
How many sides and angles does a quadrilateral has?
A quadrilateral is consisted of four sides and four angles. It also has two diagonals and four vertices.
What is the sum of interior angles of a quadrilateral?
The sum of interior angles of a quadrilateral = 360°.
What is the sum of exterior angles of a quadrilateral?
The sum of exterior angles of a quadrilateral = 360°.
Are all quadrilaterals equal?
A regular quadrilateral has 4 equal sides and 4 equal interior angles, for example: square. An irregular quadrilateral also has 4 sides and 4 angles, but not all are equal, for example: trapezium, rhombus etc.
Do quadrilaterals have right angles?
There are two quadrilaterals, whose all angles are right angles. They are – square and rectangle.
Which Quadrilateral is not a Parallelogram?
A trapezium is a quadrilateral that is not a parallelogram.
What is Cyclic Quadrilateral?
A cyclic quadrilateral is defined as that quadrilateral in which all the four vertices of the quadrilateral lie on the circumference of a circle.
|
