The perimeter of a rhombus is 40 cm and the length of one of the diagonals of the rhombus is 16 cm. What would be the area of the rhombus?
- 40 sq. cm
- 64 sq. cm
- 96 sq. cm
- 100 sq. cm
The Correct Option is C
Solution and Explanation
Calculating the Area of a Rhombus
Step 1: Formula for the Area of a Rhombus
The area A of a rhombus is given by:
Area = (1/2) × d₁ × d₂
where d₁ and d₂ are the diagonals.
Step 2: Finding the Side Length
The perimeter of the rhombus is 40 cm, so the length of each side is:
Side length = 40 / 4 = 10 cm
Step 3: Using the Pythagorean Theorem
One diagonal is given as d₁ = 16 cm. Since the diagonals bisect each other at right angles, each half-diagonal forms a right-angled triangle with the side of the rhombus.
Applying the Pythagorean theorem:
(d₁ / 2)² + (d₂ / 2)² = Side²
Substituting d₁ = 16 and Side = 10:
(16 / 2)² + (d₂ / 2)² = 10²
8² + (d₂ / 2)² = 100
64 + (d₂ / 2)² = 100
(d₂ / 2)² = 36 ⇒ d₂ / 2 = 6
d₂ = 12 cm
Step 4: Calculating the Area
Area = (1/2) × 16 × 12
= 96 sq. cm
Final Answer:
Thus, the correct answer is (C) 96 sq. cm.
Top Questions on Mensuration
The radius of a circle with centre 'P' is 10 cm. If chord AB of the circle subtends a right angle at P, find area of minor sector by using the following activity. (\(\pi = 3.14\))
Activity :
r = 10 cm, \(\theta\) = 90\(^\circ\), \(\pi\) = 3.14.
A(P-AXB) = \(\frac{\theta}{360} \times \boxed{\phantom{\pi r^2}}\) = \(\frac{\boxed{\phantom{90}}}{360} \times 3.14 \times 10^2\) = \(\frac{1}{4} \times \boxed{\phantom{314}}\) <br>
A(P-AXB) = \(\boxed{\phantom{78.5}}\) sq. cm.
- The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find: (\(\pi = 3.14\))
(i) Curved surface area of frustum.
(ii) Total surface area of the frustum.
(iii) Volume of the frustum. - How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?
- If radius of cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ...................... .
From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid.
Use $\pi = \dfrac{22}{7}, \sqrt{5} = 2.2$- CBSE Class X - 2025
- Mathematics
- Mensuration
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