Students can easily access a variety of area questions with complete explanations, which are provided below. One of the most fundamental concepts taught in elementary and secondary schools is the concept of areas of different shapes. NCERT curriculum is used to frame the questions. Students can use these questions to get a fast overview of the topics and practise them so that they will become more knowledgeable about the concept. To cross-verify your answers, look over the complete explanations for each question. To learn more about areas of different shapes, click here.
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Area Definition: The area of a two-dimensional figure is the amount of space it takes up. In other words, the amount of unit squares that cover the surface of an enclosed figure is measured by this quantity. The conventional unit of area is square centimetres, square inches, square metres, and so on. |
Go through the different types of area questions and practise them to learn the concept well.
Area Questions with Solutions
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Area Formulas: Here are the area formulas for all 2d-shapes. Circle – πr2 square units, where “r” is the radius of the circle Square – a2 square units, where a is the square’s side length Triangle – (½) × b×h square units, where b is the base and h is the height Parallelogram – Base × Height square units. Rectangle – Length × Breadth square units Rhombus – (½) × diagonal 1 × Diagonal 2 square units |
1. Find the area of a circle if its diameter is 42 cm. (Use π = 22/7)
Solution:
Given: Diameter, d = 42 cm.
Hence, Radius, r = d/2 = 42/2 = 21 cm
We know that the area of a circle = πr2 square units.
A = (22/7) × 21 × 21
A = 22 × 3 × 21
A = 1386 cm2.
Therefore, the area of the circle = 1386 cm2.
2. Calculate the radius of a circle if its area is 25π m2.
Solution:
Given: Area = 25π m2
We know that area of a circle = πr2
Hence, we can write,
25π = πr2
25 = r2
Hence, r = 5 m
Therefore, the radius of the circle is 5 m.
3. Find the area of a square whose side length is 7 cm.
Solution:
Given, Side, a = 7 cm.
As we know, the area of square = a2 square units
A = 72 cm2
A = 49 cm2
Hence, the area of the square is 49 cm2.
4. Compute the side length of a square, if its area is 121 cm2.
Solution:
Given: Area of a square = 121 cm2.
We know that, A = side2 square units
Hence,
121 = side2
Side = 11 cm
Therefore, the side length of the square is 11 cm, if its area is 121 cm2.
5. Determine the area of a rectangle, if its length is 11 cm and breadth is 9 cm.
Solution:
Given: Length = 11 cm
Breadth = 9 cm.
We know that the formula to find the area of a rectangle is:
Area = Length × Breadth square units
Area = 11 × 9 cm2
Area = 99 cm2
Therefore, the area of the rectangle is 99 cm2.
6. Compute the breadth of a rectangle if its area is 84m2 and length is 12 m.
Solution:
Given:
Area of a rectangle = 84 m2
Length = 12 m
As we know,
Rectangle’s area = Length × Breadth
Hence,
84 = 12 × Breadth
Therefore, Breadth = 84/12
Breadth = 7 m.
Hence, the breadth of the rectangle is 7 m if its area is 84 m2 and length is 12 m.
7. Find the area of a parallelogram, if its base length is 9 cm and height is 5 cm.
Solution:
Given: Base length = 9 cm
Height = 5 cm.
The formula to calculate the area of a parallelogram is:
Area = Base × Height square units.
On substituting the given values, we get
Area = 9 × 5 cm2
Area = 45 cm2
Therefore, the area of the parallelogram is 45 cm2.
8. Compute the area of a triangle, if its base measurement is 6 cm and height is 10 cm.
Solution:
Given: Base, b = 6 cm
Height, h = 10 cm.
We know that the area of a triangle = (½) × b × h square units.
Now, substitute the given values, we get
A = ½ × 6 × 10 cm2
A = 3 × 10 cm2
A = 30 cm2
Therefore, the area of the triangle is 30 cm2.
9. Determine the height of a triangle, if its base length is 8 cm and its area is 52 cm2.
Solution:
Given: Base length, b = 8 cm
Area = 52 cm2
As we know, the area of a triangle is ½ bh square units
52 = (½) × 8 × h
52 × 2 = 8 × h
104 = 8 × h
h = 104/8
h = 13
Hence, the height of the triangle is 13 cm if its base is 8 cm and its area is 52 cm2.
10. Determine the area of a rhombus if its diagonals are 7 cm and 10 cm.
Solution:
Given:
Diagonal1 = 7 cm
Diagonal2 = 10 cm
As we know,
The area of a rhombus = ½ × diagonal 1 × diagonal 2
Now, substitute the values, we get;
Area = ½ × 7 × 10 cm2
Area = 7 × 5 cm2
Area = 35 cm2
Therefore, the area of the rhombus is 35 cm2, if its diagonals are 7 cm and 10 cm.
Explore More Articles:
- Area of Triangle
- Area of Circle
- Area of Rhombus
- Rectangle Questions
- Area of Parallelogram Questions
- Quadrilaterals Questions
- Geometry Questions
Practice Questions
- Compute the area of a triangle, if its base is 14 cm and height is 10 cm.
- Determine the area of a rectangle if its length is 17 cm and breadth is 15 cm.
- Find the area of a square whose side measures 19 cm.
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