Question

HOLA MATE❤❤


⚓⚓KEEP CALM IMPORTANT QUESTION ⚓⚓
ASKER smilequeen ❤❤

question :
..................…..


find the area of the shaded region in figure Where are drawn with the centre A,B,C and , D intersect in pairs at mid points P,Q,R and S of the sides AB ,BC ,CD ,and DA respectively of the square ABCD of side 12cm [π=3.14]

❌❌DONT SPAMMING ❌❌

Answer 1

$\huge{ \bold{ \blue{solution}}}$



▪▪ The Sides of Square
AB = BC = CD = AD = 12cm

▪▪ AP , PB, CR & DR are the radii of circles with centres A , B , C & D respectively.
So, AP = PB = CR = DR = r = 6cm [ AB/2]

▪▪ Now the Area of Square

$= {a}^{2} \\ \\ = {12}^{2} \\ \\ = 144 \: {cm}^{2}$



Now the Area Of 4 quadrants ---

$= 4 \times \frac{ \pi \times {r}^{2} }{4} \\ \\ = \pi \: \times {r}^{2} \\ \\ = 3.14 \times {6}^{2} \\ \\ = 3.14 \times 36$
$\\ \\ = 113.04 \: {cm}^{2}$

$\huge{ \underline{ \bold{ \red{ \: area \: \: of \: \: a \: \: shaded \: \: region}}}}$
$\\ \\ \huge{ \bold{ = \: area \: of \: a \: square \: - \: area \: of \: 4 \: quadrants.}}$



$= 144 - 113.04 \\ \\ = 30.96 \: {cm}^{2} .............is \: the \: required \: answer.$

Answer 2

hey mate

Answer

The area formed by the four quadrants is equal to the area of a circle. So, you have to subtract the area of a circle from the area of the square.

Radius of each arc drawn = 6 cm

Area of four quadrants or area of circle = πr2

= 3.14 × 6 × 6

= 113.04 cm2

Area of square ABCD = a2

= 12 × 12 = 144 cm2

Hence, area of shaded region = 144 - 113.04

= 30.96 cm2