Advertisements
Advertisements
Question
A square is inscribed in a circle of radius 6 cm. Find the area of the square. Give your answer correct to two decimal places if `sqrt(2)` = 1.414.
Advertisements
Solution
Let the radius of the circle = r = 6cm
Now,
diagonal of a square = diameter of a circle
= 2r
= 2 x 6
= 12cm
Also,
`sqrt(2)` x side of a square = diagonal of a square
⇒ `sqrt(2)` x side = 12
⇒ side = `(12)/sqrt(12)`
= `6sqrt(2)"cm"`
∴ Area of a square
= (Side)2
= `(6sqrt(2))^2`
= 72cm2.
APPEARS IN
RELATED QUESTIONS
The base of an isosceles triangle measures 80 cm and its area is 2 `360 . cm^2` Find the perimeter of the triangle.
A carpet is laid on floor of a room 8 m by 5 m. There is border of constant width all around the carpet. If the area of the border is `12m^2` find its width.
The cost of harvesting a square field at ₹ 900 per hectare is ₹ 8100. Find the cost of putting a fence around it at ₹ 18 per meter.
Find the area of the quadrilateral ABCD in which AD = 24 cm, ∠BAD 90° and ∠BCD is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral.
The adjacent sides of a parallelogram are 32 cm and 24 cm. If the distance between the longer sides is 17.4 cm, find the distance between the shorter sides.
A regular hexagon is inscribed in a circle. If the area of hexagon is \[24\sqrt{3}\] , find the area of the circle. (Use π = 3.14)
ABCDEF is a regular hexagon with centre O (in the following figure). If the area of triangle OAB is 9 cm2, find the area of : (i) the hexagon and (ii) the circle in which the haxagon is incribed.
In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region. [Use π= 3.14]
Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made.
Thenmozhi wants to level her circular flower garden whose diameter is 49 m at the rate of ₹ 150 per m2 Find the cost of levelling
