General Questions
Practice and master this topic with our carefully crafted questions.
What happens to the area of a square when its side is halved ? Its area will :
Correct Answer: C. Become one-fourth ✅
- A. Remain same ❌
- B. Become half ❌
- C. Become one-fourth ✅ — Correct.
- D. Become double ❌
Explanation:
Let the original side of the square be a.
Original area = a².
When the side is halved:
New side = a/2.
New area = (a/2)² = a²/4.
Therefore, the new area is one-fourth of the original area.
Exam Fact:
The area of a square depends on the square of its side. If the side becomes half, the area becomes (1/2)² = 1/4.
Therefore, the correct answer is C. Become one-fourth ✅.
The area of a right - angled triangle is 40 times its base. What is its height ?
Correct Answer: C. 80 cm ✅
- A. 45 cm ❌
- B. 60 cm ❌
- C. 80 cm ✅ — Correct.
- D. Data inadequate ❌
- E. None of these ❌
Explanation:
Let the base be b cm and height be h cm.
Area of right-angled triangle = ½ × b × h.
Given area = 40b.
Therefore:
½ × b × h = 40b
Dividing both sides by b:
h/2 = 40
h = 80 cm.
Exam Fact:
When the area of a triangle is expressed as a multiple of its base, use Area = ½ × base × height and cancel the common base.
Therefore, the correct answer is C. 80 cm ✅.
Perimeter = 2 x (36 + 21 ) m = 144 m
∴ Number of flagstaffs = 144 / 3 = 38
Area = 1/2 x (Diagonal)2
= (1/2) x 5.2 x 5.2 cm2
= 13.52 cm2
Let breadth = b, length = 2b
∴ Area of rectangle = 2b x b
= 2b2
As per question.
∵ (2b - 5 ) (b + 5 ) = 2b2 + 75
⇒ 5b = 75 + 25
⇒ 5b = 100
∴ b = 100 / 5 = 20
Hence, length of the rectangle =2b
= 2 x 20
= 40 cm.
Original area = π(d/2)2
= (πd2) / 4
New area = π(2d/2)2
= πd2
Increase in area = (πd2 - πd2/4)
= 3πd2/4
∴ Required increase percent
= [(3πd2)/4 x 4/(πd2) x 100]%
= 300%
Let the diagonal of one square be (2d) cm
Then, diagonal of another square = d cm
∴ Area of first square = [ 1/2 x (2d)2] cm2
Area of second square = (1/2 x d2) cm2
∴ Ratio of area = (2d)2/ d2
= 4/1 = 4 : 1
Area of equilateral triangle = √3/4 a2 = 4√3.
⇒ a2 = 16
∴ a = 4 cm
Given that, a = 6 cm, b = 4 cm and c = 5 cm
Required perimeter = a + b + c
= 6 + 4 + 5 cm
= 15 cm
Given that, area = 10 sq cm,
Perpendicular = 20 cm and Base = ?
Area = (Base x Perpendicular) / 2
⇒ 10 = (Base x 20) / 2
∴ Base = 1 cm