Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4 (√2 - l) cm, then the area, in sq cm, of the triangle ABC is
- 10
- 19
- 18
- 16
The Correct Option is D
Solution and Explanation
As P is equidistant from the sides, P is the in center of the triangle.
r is the in radius of the triangle, viz. 4(√2 - 1) cm
Let the sides of the triangle be a, a, a √2
As Δ=1/2 (a)(a) = r(s),
a2/2 = 4(√2-1)(a+a+a√2)/2
⇒ a = 4√2
Area = 1/2(a2) = 16 sq.units
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
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