Question

In the given figure (not drawn to scale), all 6 quadrants are identical. Find the shaded area.

231 cm²
63 cm²
42 cm²
113 cm²​

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

In the given figure (not drawn to scale), all 6 quadrants are identical. Find the shaded area.

⚪ 231 cm²

⚪ 42 cm²

⚪ 63 cm²

⚪ 113 cm²

★═════════════════★

♣ ᴀɴꜱᴡᴇʀ :

Area of shaded region = 63 cm²

⚪ 231 cm²

⚪ 42 cm²

⚪ 63 cm² ✔️

⚪ 113 cm²

★═════════════════★

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

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# Calculate area of 6 quadrants

Radius of one quadrant = $\sf{{\dfrac{21}{3}}$ = 7 cm

∴ Area of one quadrant = $\sf{\dfrac{1}{4}}$ × π × (7)² cm²

Area of one quadrant = $\sf{\dfrac{1}{4}}$ × $\sf{\dfrac{22}{7}}$ × (7)² cm²

Area of one quadrant = $\sf{\dfrac{1}{4}}$ × $\sf{\dfrac{22}{7}}$ × 49 cm²

Area of one quadrant = $\sf{\dfrac{22}{28}}$ × 49 cm²

Area of one quadrant = $\sf{\dfrac{1078}{28}}$  cm²

When simplified to it's lowest form,

Area of one quadrant = $\sf{\dfrac{77}{2}}$ cm²

So, Area of 6 quadrants =  6 ×  $\sf{\dfrac{77}{2}}$ cm² = 231 cm²

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# Calculate area of Rectangle

Area of rectangle = Length × Breadth

Area of rectangle = 21 × 14 cm²

Area of rectangle = 294 cm²

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 21 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 14 cm}\put(-0.5,-0.4){\bf C}\put(-0.5,3.2){\bf A}\put(5.3,-0.4){\bf D}\put(5.3,3.2){\bf B}\end{picture}$

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Therefore,

Area of Shaded Region

= 294 cm² - 231 cm²

= 63 cm²

Answer 2

113cm2 is the answer of question