A square ODEF is inscribed in a quadrant OPEQ of a circle and OD= 14√2 cm. Aarthi said that "the area of shaded region is 224cm^2" Do you Agree ?
Answers
Given: OD= 14√2 cm, square ODEF is inscribed in a quadrant OPEQ of a circle
To find: Area of the shaded region which is the remaining part of the quadrant in which the square is inscribed?
Solution:
- Now as we have given that side of the square id 14√2 cm, so from this we can find the diagonal which will be equal to the radius of the circle.
- So, diagonal = √(14√2² + 14√2²)
= √(784)
= 28 cm
- So now, radius is equal to 28 cm, so area of quadrant is πr²/4
= ( 3.14 x 28 x 28 ) / 4
= 615.44 cm²
- Area of square = side²
= 14√2²
= 392 cm²
- Now the area of the shaded region is:
area of quadrant - Area of square
615.44 cm² - 392 cm²
293.44 cm²
Answer:
So the area of the shaded region is 293.44 cm².
Step-by-step explanation:
Given A square ODEF is inscribed in a quadrant OPEQ of a circle and OD= 14√2 cm. Aarthi said that "the area of shaded region is 224cm^2 Do you Agree ?
- Area of shaded region = Area of quadrant OPEQ – Area of square ODEF
- Now Area of square = side^2
- = (14 √2)^2
- = 392 cm^2
- Now we need to find the radius and all angles of a square are 90 degree
- So angle EDO = 90 degree
- Hence triangle OED is a right angle.
- Now by using Pythagoras theorem we get
- OE^2 = DE^2 + OD^2
- = (14√2)^2 + (14√2)^2
- = 392 + 392
- OE^2 = 784
- OE = √784
- OE = 28
- So radius = 28
- Now area of quadrant = ¼ x area of circle
- = ¼ x π r^2
- = ¼ x 22/7 x 28 x 28
- = 616 cm^2
- Area of shaded region = Area of quadrant OPEQ – area of square ODEF
- = 616 – 392
- = 224 cm^2
- Therefore area of shaded region = 224 cm^2
