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Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > Unit Test (Solutions): Perimeter and Area
Unit Test (Solutions): Perimeter and Area | Mathematics (Maths) Class 7 PDF Download
Q1: What is the area of a parallelogram with a base of 6 cm and a height of 4 cm? (1 Mark)
(a) 24 cm²
(b) 10 cm²
(c) 16 cm²
(d) 12 cm²
Ans: (a) 24 cm²
Sol: The area of a parallelogram is given by Area = base × height.
Area = 6 cm × 4 cm = 24 cm².
Q2: A triangle has a base of 8 cm and a height of 5 cm. What is its area? (1 Mark)
(a) 12 cm²
(b) 20 cm²
(c) 40 cm²
(d) 16 cm²
Ans: (a) 12 cm²
Sol: The area of a triangle is given by Area = (1/2) × base × height.
Area = (1/2) × 8 cm × 5 cm = 12 cm².
Q3: The perimeter of a rectangle is 20 cm. If the length is 7 cm, what is the breadth? (1 Mark)
(a) 6 cm
(b) 5 cm
(c) 3 cm
(d) 4 cm
Ans: (b) 5 cm
Sol: The perimeter of a rectangle is given by Perimeter = 2 × (length + breadth).
20 cm = 2 × (7 cm + breadth).
So, breadth = (20 / 2) - 7 = 10 - 7 = 3 cm.
Q4: What is the area of a circle with a radius of 7 cm? (Use π = 3.14). (1 Mark)
(a) 154 cm²
(b) 140 cm²
(c) 49 cm²
(d) 75 cm²
Ans: (a) 154 cm²
Sol: The area of a circle is given by Area = π × radius².
Area = 3.14 × (7 cm)² = 3.14 × 49 = 154 cm².
Q5: A parallelogram has a base of 10 cm and sides of 6 cm. What is its perimeter? (1 Mark)
(a) 32 cm
(b) 24 cm
(c) 26 cm
(d) 20 cm
Ans: (b) 24 cm
Sol: The perimeter of a parallelogram is given by Perimeter = 2 × (base + side).
Perimeter = 2 × (10 cm + 6 cm) = 2 × 16 cm = 24 cm.
Q6: Calculate the perimeter of the figure. The figure is a semicircle, including its diameter. (2 Marks)
Ans: As per the given question,
The Diameter of the semi-circle = 10 cm
Radius = r = d/2 = 10/2 = 5 cm
Circumference of the semi-circle = 22/7 × 5 = 110/7 = 15.71 cm.
To calculate the perimeter of the above figure,
Perimeter of the semi-circle = semi-circle circumference + semicircle diameter 15.71 + 10 = 25.71 cm
Q7: Find the area of the triangle(in cm2) with base 6 cm and height 4 cm. (2 Marks)
Ans: Here, in △ABC, BC and AD are the base and the height of the triangle.
∴ BC = 6cm and AD = 4cm
⇒ Area of △ABC = 1/2 × BC × AD
= 1/2 x 6 x 4
= 12 cm2
Q8: Find the area and circumference of the circle whose radius is: (2 Marks)
(a) 3cm
(b) 12cm
Ans:
(a) Given, radius = 3cm
C = 2πr
C = Circumference
C = 2 × 22/7 × 3
C = 132/7 cm
Area = πr²
Area = 22/7 × (3)²
Area = 22/7 × 9
Area = 198/7 sq. cm
Area = 28.29 sq. cm
(b) Given, radius = 12cm
C = 2πr
C = 2 × 22/7 × 12
C = 528/7 cm
Area = πr²
Area = 22/7 × (12)²
Area = 22/7 × 144
Area = 3168/7 sq. cm
Area = 452.57 sq. cm
Q9: The rate of painting is Rs 20/m². Find the cost of painting a circular wall with a diameter of 2.4 m. (3 Marks)
Ans: As per the given question,
The diameter of the circular wall = 2.4 m
As we know the
Radius = r = d/2 = 2.4 / 2 = 1.2 m
Area of the circular wall will be 3.14 × 1.2 × 1.2 = 4.52256 m²
The cost of painting 1 m² area = Rs 20
So for calculating the 4.52256 m² area = Rs 20 × 4.52256 = 90.4512
So to paint the area of 4.52256 m², the cost incurred is Rs 90.4512
Q10: The right-angled triangle is XYZ, given. This is right-angled at X. XY is perpendicular to ZY. If XY = 8 cm, ZY = 17 cm, and XZ = 15 cm, calculate the area of triangle XYZ. Also, calculate the length of XY. (3 Marks)
Ans: According to the given question,
XY = 8 cm
ZY = 17 cm
XZ = 15 cm
We know that,
Area of triangle XYZ = ½ × Base × height
= ½ × XY × XZ
= ½ × 8 × 15 = 4 × 15 = 60 cm²
Now,
Area of triangle XYZ = ½ × Base × height
60 = ½ × XY × ZY
60 = ½ × XY × 17
60 × 2 / 17 = XY
XY = 120 / 17 = 7.06 cm
Q11: DL and BM are the heights on sides AB and AD respectively of ABCE parallelogram. Let us suppose the area of the parallelogram is 1470 cm2, AB = 35 cm and AD = 49 cm. Calculate the length of the BM and the DL. (3 Marks)
Ans: According to the question given above,
The Area of the parallelogram = 1470 cm2
AB = 35 cm
AD = 49 cm
Then
It is clear that
The Area of the parallelogram = base × height
1470 = AB × BM
1470 = 35 × DL
1470/35 = DL
DL = 42 cm
Area of the parallelogram = base × height
1470 = AD × BM
1470 = 49 × BM
BM = 1470/49
BM = 30 cm
Q12: Find the area of a flat circular ring formed by two concentric circles (circles with the same center) whose radii are 12 cm and 7 cm. (5 Marks)
Ans:
Area of the region between two concentric circles with the radius of the outer circle R, and the inner circle r = π (R² − r²)
Hence, the area of a flat circular ring formed by two concentric circles whose radii are 12 cm and 7 cm
= π (12² − 7²)
= 22/7(144 − 49)
= 22/7 × 95
= 660/7
= 94.29 cm²
Q13: Look at the figure given below, the circular card sheet has a radius of 14 cm. Two circles are removed of radius 3.5 cm and a rectangle is also removed, the length and breadth of the rectangle are 3 cm and 1cm respectively. Given the value = 22/7, calculate the area of the remaining sheet by applying the suitable formulas. (5 Marks)
Ans: From the question, it is clear that
The Radius of the circular sheet is 14 cm
The Radius of the two small circles is 3.5 cm
The length of the rectangle is 3 cm
Breadth of the rectangle is 1 cm
To calculate the remaining area,
The Area of the circular card sheet = 22/4 × 14 × 14 = 22 × 2 × 14 = 616 cm2
To calculate the area of the two small circles,
= 2 × (22/7 × 3.5 × 3.5)
=2 × ((22/7) 12.25)
= 2 × 38.5
= 77 cm2
To calculate the area of the rectangle = length × breadth = 3 × 1 = 3 cm2
To calculate the area of the remaining part,
Area of card sheet – ( area of 2 small circles + rectangle area)
= 616 – (77 + 3)
= 616 – 80
The document Unit Test (Solutions): Perimeter and Area | Mathematics (Maths) Class 7 is a part of the Class 7 Course Mathematics (Maths) Class 7.
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FAQs on Unit Test (Solutions): Perimeter and Area - Mathematics (Maths) Class 7
| 1. What is the formula to calculate the perimeter of a rectangle? |  |
| 2. How do you find the area of a triangle? | |
Ans. The area of a triangle can be found using the formula A = (1/2) × base × height, where 'base' is the length of the triangle's base and 'height' is the perpendicular height from the base to the opposite vertex.
| 3. What is the difference between perimeter and area? | |
Ans. Perimeter refers to the total distance around a two-dimensional shape, while area measures the amount of space contained within that shape. The perimeter is a linear measurement, while area is a square measurement.
| 4. How do you calculate the area of a circle? | |
Ans. The area of a circle can be calculated using the formula A = πr², where 'r' is the radius of the circle and π (pi) is approximately equal to 3.14.
| 5. Can you give an example of calculating the perimeter and area of a square? | |
Ans. For a square with a side length of 's', the perimeter is calculated using P = 4s, and the area is calculated using A = s². For example, if the side length is 5 units, the perimeter would be 20 units and the area would be 25 square units.
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