Let the each side of equilateral triangle = a Area of equilateral triangle = 17320.5 cm² ⇒ √3/4 a² = 17320.5 ⇒ 1.73205/4 a² ⇒ 17320.5 ⇒ a² = 40000 ⇒ a = 200 Area of sector ADEF = θ/360° × πr² = 60°/360° × 22/7(100)² = 1/6 × 3.14 × 100 × 100 = 15700/3 cm² Area of shaded region = Area of equilateral tRead more
Let the each side of equilateral triangle = a
Area of equilateral triangle = 17320.5 cm²
⇒ √3/4 a² = 17320.5 ⇒ 1.73205/4 a² ⇒ 17320.5 ⇒ a² = 40000 ⇒ a = 200
Area of sector ADEF
= θ/360° × πr² = 60°/360° × 22/7(100)² = 1/6 × 3.14 × 100 × 100 = 15700/3 cm²
Area of shaded region = Area of equilateral triangle – Area of three sectors
= 17320.5 cm² – 3 x 15700/3 cm²
= 17320.5 cm² – 15700 cm²
= 1620.5 cm²
Radius of circle = 7 cm Area of one circular design πr² = π(7)² = 22/7 × 7 × 7 = 154 cm² Side of square = 42 cm Area of squre = (Side)² = (42)² = 1764cm² The area of the remaining portion = Area of square - Area of 9 circular designs = 1764 - 9 × 154 = 196 1386 = 378 cm²
Radius of circle = 7 cm
Area of one circular design
πr² = π(7)² = 22/7 × 7 × 7 = 154 cm²
Side of square = 42 cm
Area of squre = (Side)² = (42)² = 1764cm²
The area of the remaining portion = Area of square – Area of 9 circular designs
= 1764 – 9 × 154 = 196 1386 = 378 cm²
In A0AB, OB² = OA² + AB² ⇒ OB² = (20)² + (20)² ⇒ OB² = 400+ 400 ⇒ OB² = 800 ⇒ OB = √800 Radius of quadrant = 20√2 cm Area of quadrant = 90°/360° × πr² = 1/4 × π(20√2)² = 1/4 × 3.14 × 20√2 × 20√2 = 628 cm² Area of square = (Side)² = (20)² = 400 cm² Area of shaded region = Area of quadrant - Area of sRead more
In A0AB,
OB² = OA² + AB² ⇒ OB² = (20)² + (20)² ⇒ OB² = 400+ 400
⇒ OB² = 800 ⇒ OB = √800
Radius of quadrant = 20√2 cm
Area of quadrant
= 90°/360° × πr² = 1/4 × π(20√2)²
= 1/4 × 3.14 × 20√2 × 20√2 = 628 cm²
Area of square
= (Side)² = (20)² = 400 cm²
Area of shaded region = Area of quadrant – Area of square
= 628 – 400 = 228 cm²
Radius of smaller circle = 7/2 cm Area of smaller circle = πr² = π(7/2)² = 22/7 × 7/2 × 7/2 = 77/2 cm² Radius of larger circle = 7 cm Area of semicircle AECFB = 1/2 × πr² = π(7)² = 1/2 × 22/7 7 × 7 = 77 cm² Area of triangle ACB = 1/2 × AB × OC = 1/2 × 14 × 7 = 49 cm² Area of Shaded Region = Area ofRead more
Radius of smaller circle = 7/2 cm
Area of smaller circle = πr² = π(7/2)² = 22/7 × 7/2 × 7/2 = 77/2 cm²
Radius of larger circle = 7 cm
Area of semicircle AECFB
= 1/2 × πr² = π(7)² = 1/2 × 22/7 7 × 7 = 77 cm²
Area of triangle ACB
= 1/2 × AB × OC = 1/2 × 14 × 7 = 49 cm²
Area of Shaded Region
= Area of smaller circle + Area of semicircle AECFB – Area of triangle ACB
= (77/2 + 77 – 49) cm² = (38.5 + 28) cm² = 66.5 cm²
Here you can see the video explanation of this question for better understanding😄👇
Find the area of the shaded region.
Area of shaded region = Area of sector OAEB - Area of sector OCFD = 30°/360° × π × (21)² - 30°/360° × π × 7² = 1/12 × π[441 - 49] = 1/12 × 22/7 × 392 = 308/3 cm²
Area of shaded region = Area of sector OAEB – Area of sector OCFD
See less= 30°/360° × π × (21)² – 30°/360° × π × 7²
= 1/12 × π[441 – 49]
= 1/12 × 22/7 × 392 = 308/3 cm²
The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Figure).
Let the each side of equilateral triangle = a Area of equilateral triangle = 17320.5 cm² ⇒ √3/4 a² = 17320.5 ⇒ 1.73205/4 a² ⇒ 17320.5 ⇒ a² = 40000 ⇒ a = 200 Area of sector ADEF = θ/360° × πr² = 60°/360° × 22/7(100)² = 1/6 × 3.14 × 100 × 100 = 15700/3 cm² Area of shaded region = Area of equilateral tRead more
Let the each side of equilateral triangle = a
See lessArea of equilateral triangle = 17320.5 cm²
⇒ √3/4 a² = 17320.5 ⇒ 1.73205/4 a² ⇒ 17320.5 ⇒ a² = 40000 ⇒ a = 200
Area of sector ADEF
= θ/360° × πr² = 60°/360° × 22/7(100)² = 1/6 × 3.14 × 100 × 100 = 15700/3 cm²
Area of shaded region = Area of equilateral triangle – Area of three sectors
= 17320.5 cm² – 3 x 15700/3 cm²
= 17320.5 cm² – 15700 cm²
= 1620.5 cm²
In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, fiIn Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm,
Radius of circle = 7 cm Area of one circular design πr² = π(7)² = 22/7 × 7 × 7 = 154 cm² Side of square = 42 cm Area of squre = (Side)² = (42)² = 1764cm² The area of the remaining portion = Area of square - Area of 9 circular designs = 1764 - 9 × 154 = 196 1386 = 378 cm²
Radius of circle = 7 cm
See lessArea of one circular design
πr² = π(7)² = 22/7 × 7 × 7 = 154 cm²
Side of square = 42 cm
Area of squre = (Side)² = (42)² = 1764cm²
The area of the remaining portion = Area of square – Area of 9 circular designs
= 1764 – 9 × 154 = 196 1386 = 378 cm²
In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm,
In A0AB, OB² = OA² + AB² ⇒ OB² = (20)² + (20)² ⇒ OB² = 400+ 400 ⇒ OB² = 800 ⇒ OB = √800 Radius of quadrant = 20√2 cm Area of quadrant = 90°/360° × πr² = 1/4 × π(20√2)² = 1/4 × 3.14 × 20√2 × 20√2 = 628 cm² Area of square = (Side)² = (20)² = 400 cm² Area of shaded region = Area of quadrant - Area of sRead more
In A0AB,
See lessOB² = OA² + AB² ⇒ OB² = (20)² + (20)² ⇒ OB² = 400+ 400
⇒ OB² = 800 ⇒ OB = √800
Radius of quadrant = 20√2 cm
Area of quadrant
= 90°/360° × πr² = 1/4 × π(20√2)²
= 1/4 × 3.14 × 20√2 × 20√2 = 628 cm²
Area of square
= (Side)² = (20)² = 400 cm²
Area of shaded region = Area of quadrant – Area of square
= 628 – 400 = 228 cm²
In Figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Radius of smaller circle = 7/2 cm Area of smaller circle = πr² = π(7/2)² = 22/7 × 7/2 × 7/2 = 77/2 cm² Radius of larger circle = 7 cm Area of semicircle AECFB = 1/2 × πr² = π(7)² = 1/2 × 22/7 7 × 7 = 77 cm² Area of triangle ACB = 1/2 × AB × OC = 1/2 × 14 × 7 = 49 cm² Area of Shaded Region = Area ofRead more
Radius of smaller circle = 7/2 cm
Area of smaller circle = πr² = π(7/2)² = 22/7 × 7/2 × 7/2 = 77/2 cm²
Radius of larger circle = 7 cm
Area of semicircle AECFB
= 1/2 × πr² = π(7)² = 1/2 × 22/7 7 × 7 = 77 cm²
Area of triangle ACB
= 1/2 × AB × OC = 1/2 × 14 × 7 = 49 cm²
Area of Shaded Region
= Area of smaller circle + Area of semicircle AECFB – Area of triangle ACB
= (77/2 + 77 – 49) cm² = (38.5 + 28) cm² = 66.5 cm²
Here you can see the video explanation of this question for better understanding😄👇
See less