The length of sides of a triangular field are 32 m, 27 m and 11 m. What is the approximate area of triangle?
- 132 m2
- 142 m2
- 152 m2
- 162 m2
The Correct Option is B
Solution and Explanation
Calculating the Area of a Triangle Using Heron's Formula
Step 1: Heron's Formula
The area A of a triangle is given by:
A = √(s (s - a) (s - b) (s - c))
where a, b, and c are the sides of the triangle, and s is the semi-perimeter:
Step 2: Calculate the Semi-Perimeter (s)
s = (a + b + c) / 2
s = (32 + 27 + 11) / 2 = 35
Step 3: Apply Heron’s Formula
A = √(35 × (35 - 32) × (35 - 27) × (35 - 11))
= √(35 × 3 × 8 × 24)
= √20160
≈ 142 m²
Final Answer:
Thus, the correct answer is (B) 142 m².
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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