Question-87671

Question Number 87671 by TawaTawa1 last updated on 05/Apr/20

Commented by TawaTawa1 last updated on 05/Apr/20

I got 10.5 m^{2} but am not sure .

Please help me check .

Commented by Tony Lin last updated on 05/Apr/20

7^{2} \times \frac{2 π}{3} \times \frac{1}{2} - 7^{2} \times \frac{\sqrt{3}}{4}

= 49 (\frac{π}{3} - \frac{\sqrt{3}}{4})

\approx 30 ({c m}^{2})

= 0.003 (m^{2})

0.0049 - 0.003 = 0.0019 (m^{2})

Commented by TawaTawa1 last updated on 05/Apr/20

God bless you sir

Answered by mr W last updated on 05/Apr/20

A_{s h a d e} = 7 \times 7 - 2 \times \frac{π \times 7^{2}}{6} + \frac{7^{2} \times \sqrt{3}}{4}

= 49 - \frac{49 π}{3} + \frac{49 \sqrt{3}}{4}

\approx 18.9 {c m}^{2} = 0.00189 m^{2}

Commented by TawaTawa1 last updated on 05/Apr/20

God bless you sir

Commented by TawaTawa1 last updated on 05/Apr/20

Sir, have been trying to understand - 2 \times \frac{π \times 7^{2}}{6} + \frac{7^{2} \times \sqrt{3}}{4}

But since i did not understand .

Please help me explain when you are chanced sir .

Please .

Commented by mr W last updated on 05/Apr/20

Commented by mr W last updated on 05/Apr/20

Commented by mr W last updated on 05/Apr/20

A_{1} = s q u a r e = 7 \times 7

A_{2} = s e c t o r = \frac{c i r c l e}{6} = \frac{π \times 7^{2}}{6}

A_{3} = e q u i l a t e r a l t r i a n g l e = \frac{1}{2} \times 7 \times \frac{\sqrt{3} \times 7}{2} = \frac{7^{2} \sqrt{3}}{4}

A_{s h a d e} = A_{1} - 2 A_{2} + A_{3}

= 7 \times 7 - 2 \times \frac{7^{2} π}{6} + \frac{7^{2} \sqrt{3}}{4}

= 49 - \frac{49 π}{3} + \frac{49 \sqrt{3}}{4}

Commented by TawaTawa1 last updated on 05/Apr/20

Hahaha . Am happy .

I understand now, God will be helping you too sir .