Kuis 100xf72 Points Dari Stingray:Kalo Lagi Pusing Mending Gk Usah Dijawab! #Part2, Jika Diameter Lingkaran Adalah 288 Cm Maka, Buktikan Luas Yg Diarsir Adalah (4608221a3 + 13824 + 3456221a2) Cmxb2, Tantangan (tidak Wajib):, Kerjakan Tanpa Trigonometri!, Yang Ngasal Direport!!!

Kuis 100÷2 Points dari Stingray:Kalo lagi pusing mending gk usah dijawab! #Part2

Jika diameter Lingkaran adalah 288 cm maka
Buktikan Luas yg Diarsir Adalah (4608√3 + 13824 + 3456√2) cm²

Tantangan (tidak wajib):
Kerjakan tanpa Trigonometri!

Yang Ngasal Direport!!!

Jawab:

Luas arsir =

$\huge\boxed{\boxed{\sf{-20736\left(13\sqrt{3}-24\right)}cm^2}}$

$\large\boxed{\sf{\approx 30.758,53\:\:cm^{2} }}$

Kamu salah hitung

Penjelasan dengan langkah-langkah:

Langkah-langkah pertama ada di gambar,

lalu lanjut disini.

→ → cari panjang oL =

$\boxed{\sf{\frac{oL}{sin\left(j\right)}=\frac{144}{sin\left(L\right)}}}\\\\\boxed{\sf{\frac{oL}{sin\left(15\right)}=\frac{144}{sin\left(105\right)}}}\\\boxed{\sf{oL = \frac{144\cdot \frac{\sqrt{6}-\sqrt{2}}{4}}{\frac{\sqrt{3}+1}{2\sqrt{2}}}}}\\\boxed{\sf{oL =\frac{144\cdot \frac{\sqrt{6}-\sqrt{2}}{4}\cdot \:2\sqrt{2}}{\sqrt{3}+1}}}$

$\boxed{\sf{oL = \frac{288\sqrt{2}\frac{\sqrt{6}-\sqrt{2}}{4}}{\sqrt{3}+1}}}\\\boxed{\sf{oL = \frac{144\sqrt{3}-144}{\sqrt{3}+1}}}\\\boxed{\sf{oL = \frac{\left(144\sqrt{3}-144\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}}}\\\boxed{\sf{oL = \frac{576-288\sqrt{3}}{2}}}\\\boxed{\sf{oL = \frac{288\left(2-\sqrt{3}\right)}{2}}}\\\large\boxed{\sf{oL = 144\left(2-\sqrt{3}\right)\:\:cm}}\\$

Luas segi-12 didalamnya lagi =

$\boxed{\sf{12\cdot\frac{oL^2\cdot sin \left(o\right)}{2}}}\\\\\boxed{\sf{12\cdot\frac{(144\left(2-\sqrt{3}\right))^2\cdot sin \left(30\right)}{2}}}\\\\\boxed{\sf{12\cdot \frac{20736\left(7-4\sqrt{3}\right)\cdot \frac{1}{2}}{2}}}\\\\\boxed{\sf{12\cdot \:5184\left(7-4\sqrt{3}\right)}}\\\\\large\boxed{\sf{Luas\:\:segi-12 = 62208\left(7-4\sqrt{3}\right)\:\:cm^2}}$

Daerah arsir total =

$\large\boxed{\boxed{\sf{-20736\left(\sqrt{3}-3\right) + 62208\left(7-4\sqrt{3}\right)}}} =\\\large\boxed{\sf{-20736\sqrt{3}+62208+435456-248832\sqrt{3}}} =$