Short Answer Type Questions :-
1. The base of a parallelogram is 4 cm. Its area is 12 cm². What is the length of its height?
2. The side of a square is 1.5 cm. What is its area?
3. The area of a rectangle is 20 cm². If its length is 5 cm, what is its breadth?
4. The area of a right-angled triangle is 20 cm². If its altitude is 4 cm, then what is its base?
5. The radius of a circle is 2 cm. What is its circumference?
6. The diameter of a circle is 1 cm. What is its circumference?
7. What is the area of a circle whose radius is 7 cm?
8. What is the area of a circle whose diameter is 2 cm?
Answers
Answer:
1) The length of the height is 3 cm.
2) The area of square is 2.25 cm².
3) The breadth of rectangle is 4 cm.
4) The base of triangle is 10 cm.
5) The circumference of the circle is 4π cm or 12.56 cm.
6) The circumference of the circle is π cm or 3.14 cm.
7) The area of circle is 49π cm² or 154 cm².
8) The area of circle is π cm² or 3.14 cm².
Step-by-step explanation:
1) Given: Base of parallelogram = 4 cm and Area of parallelogram = 12 cm².
Let the length of its height be y cm.
w.k.t., area of parallelogram with base b and height h is (b×h).
⇒ 12 = 4×y
⇒ y = 12/4 = 3 cm
2) Given: Side of square = 1.5 cm
w.k.t., area of square with side length a is a².
⇒ Area of square = (1.5)²
⇒ Area of square = 2.25 cm²
3) Given: Area of rectangle = 20 cm² and length of rectangle = 5 cm.
Let the breadth of rectangle be y cm.
w.k.t., area of rectangle of length l and breadth b is l×b.
⇒ 20 = 5×y
⇒ y = 20/5 = 4 cm
4) Given: Area of right-angled triangle = 20 cm² and its altitude = 4 cm.
Let the base of triangle be y cm.
w.k.t., area of right-angled triangle with base b and altitude or height h is (b×h)/2.
⇒ 20 = (y×4)/2
⇒ 40 = 4y
⇒ y = 40/4 = 10 cm
5) Given: Radius of the circle = 2 cm.
w.k.t., circumference of circle of radius r is 2πr.
⇒ Circumference of circle = 2π×2
⇒ Circumference of circle = 4π cm
⇒ Circumference of circle = 4×3.14 = 12.56 cm
6) Given: Diameter of the circle = 1 cm.
⇒ Radius of circle = 1/2 = 0.5 cm
w.k.t., circumference of circle of radius r is 2πr.
⇒ Circumference of circle = 2π×0.5
⇒ Circumference of circle = π cm = 3.14 cm
7) Given: Radius of the circle = 7 cm.
w.k.t., area of circle of radius r is πr².
⇒ Area of circle = π×(7)²
⇒ Area of circle = 49π cm² = 154 cm²
8) Given: Diameter of the circle = 2 cm.
⇒ Radius of circle = 2/2 = 1 cm
w.k.t., area of circle of radius r is πr².
⇒ Area of circle = π×(1)²
⇒ Area of circle = π cm² = 3.14 cm²
(1) The base of a parallelogram is 4 cm. Its area is 12 cm². What is the length of its height?
(1) Base × Height
= Area 12/4
= 3 cm.
(2) The side of a square is 1.5 cm. What is its area?
(2) Side of Square = 1.5 cm Area of Square
= a × a
= 1.5 x 1.5 cm
= 2.25 cm.
(3) The area of a rectangle is 20 cm². If its length is 5 cm, what is its breadth?
(3) Area = 20 cm Length
5 cm Area = length × breadth
20 = 5 x breadth
Breadth = 20/5
= 4 cm
(4) The area of a right-angled triangle is 20 cm². If its altitude is 4 cm, then what is its base?
(4) ½ × base × height
Area = Base × 4
= 2 × 20
Base = 10 cm
(5) The radius of a circle is 2 cm. What is its circumference?
(5) We know that,
Circumference of circle = 2πr
Put the given values in the formula.
=> 2 × 22/7 × 2
=> 88/7
Ans : 12.57
(6) The diameter of a circle is 1 cm. What is its circumference?
=> We know that, Circumference of circle = 2πr. So, radius = diameter/2
=> radius, r = 1/2 => Radius, r = 0.5cm.
Now, To find the circumference of a circle
=> 2πr => 2 × 22/7 × 0.5
We know that, 0.5 can be written as 1/2.
=> 2 × 22/7 × 1/2
Ans : 3.14
(7) What is the area of a circle whose radius is 7 cm?
Area of a circle = πr²
Area of the circle = π × 7 × 7
= 49π
Ans : 49π
(8) What is the area of a circle whose diameter is 2 cm?
Diameter = 2 cm
Radius = Diameter/ 2
= 2/2 = 1 cm
Area of Circle = 22/7
= 22/7 × 1 = 3.14 cm²