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Area of Triangles

In the figure...

Question

In the figure, from one handkerchief from four corners, sectors P, Q, R, S each of 2 cm are cut, whose sum is P + Q + R + S = $A_{1}$ and a circle of diameter 4 cm from the centre is cut whose area is $A_{2}$ , then .................... is possible

A_{1} \neq A

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A_{1} < A_{2}

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A_{1} > A_{2}

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A_{1} = A_{2}

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Solution

The correct option is C $A_{1} = A_{2}$
Handkerchief is in the form of a square.
Hence, $θ = 90^{o}$
Radius of each minor sector = r = 2cm
$∴$ Area of four minor sectors $= 4 \times \frac{π r^{2} θ}{360}$
$∴ A_{1} = \frac{4 \times 22 \times 2 \times 2 \times 90}{7 \times 360} = \frac{88}{7} c m^{2}$
For the circle in the middle of the square, diameter d = 4 cm
$∴$ Radius of the circle $= \frac{4}{2} = 2 c m$
$∴$ Area of the circle in the middle, $A_{2} = \frac{22}{7} \times 2 \times = \frac{88}{7} c m^{2}$
$∴ A_{1} = A_{2}$

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Similar questions

Q. In the figure, from the handkerchief from four corners, sectors P, Q, R and S each of

2 c m

are cut, whose sum is

P + Q + R + S = A_{1}

and a circle of diameter

4 c m

from the centre is cut whose area is

A_{2}

, then ______ is possible.

If $a_{1}, a_{2}, a_{3}, a_{4}$ are the magnitude of the coordinates at which the circle cuts the axes as shown in the figure. Then what the sum of x and y intercepts.

Q. The chord of the contact of tangents from a point

P

to a circle passes through

Q

(

Q

lies outside the circle). If

a_{1}

and

a_{2}

are the lengths of the tangents from

P

and

Q

to the circle respectively, then

P Q

is equal to

Q. Let

a_{1}, a_{2}, a_{3} \dots

be terms of A.P.

I f \frac{a_{1} + a_{2} + \dots a_{p}}{a_{1} + a_{2} + \dots + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q,

then

\frac{a_{6}}{a_{21}}

equal

Q. Let

a_{1}, a_{2}, a_{3}, . . . . .

be terms of an

A . P .

\frac{a_{1} + a_{2} + . . . + a_{q}}{a_{1} + a_{2} + . . . + a_{q}} = \frac{p^{2}}{q^{2}}, (p \neq q)

then find

\frac{a_{6}}{a_{21}}

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In the figure, from one handkerchief from four corners, sectors P, Q, R, S each of 2 cm are cut, whose sum is P + Q + R + S = A1 and a circle of diameter 4 cm from the centre is cut whose area is A2, then .................... is possible

In the figure, from one handkerchief from four corners, sectors P, Q, R, S each of 2 cm are cut, whose sum is P + Q + R + S = $A_{1}$ and a circle of diameter 4 cm from the centre is cut whose area is $A_{2}$ , then .................... is possible