10. Perhatikan gambar berikut.

C
Luas daerah yang diarsir adalah
16 cm
32 cm
b. 162 cm d. 322 cm

10. Perhatikan gambar berikut.

Jawaban:

Panjang BD

$sin( alpha ) = frac{bd}{bc} \ sin(30) = frac{bd}{16} \ frac{1}{2} = frac{bd}{16} \ bd = 16 times frac{1}{2} \ bd = 8 : cm$

Panjang BD 8 cm

Panjang DC

$cos( alpha ) = frac{dc}{bc} \ cos(30) = frac{dc}{16} \ frac{1}{2} sqrt{3} = frac{dc}{16} \ dc = 16 times frac{1}{2} sqrt{3} = 8 sqrt{3} : cm$

Panjang DC 8√3 cm

——————————–

Panjang AD

$sin( alpha ) = frac{bd}{ad} \ sin(45) = frac{8}{ad} \ frac{1}{2} sqrt{2} = frac{8}{ad} \ ad = 8 times frac{1}{2} sqrt{2} \ ad = 4 sqrt{2} : cm$

Panjang AD 4√2 cm

Panjang AB

$cos( alpha ) = frac{ab}{ad} \ cos(45) = frac{ab}{4 sqrt{2} } \ frac{1}{2} sqrt{2} = frac{ab}{4 sqrt{2} } \ ab = 4 sqrt{2} times frac{1}{2} sqrt{2} \ ab = 4 : cm$

Panjang AB 4 cm

Luas daerah yang diarsir =

$frac{1}{2} times a times t \ frac{1}{2} times 4 times 8 \ 1 times 2 times 8 = 16 : c {m}^{2} \ atau \ frac{1}{2} times 4 times 8 \ frac{1}{2} times 32 \ frac{32}{2} = 16 : c {m}^{2}$

ATAU

$frac{a times t}{2} \ frac{4 times 8}{2} \ frac{32}{2} = 16 : c {m}^{2}$

Jadi, luas daerah yang diarsir 16 cm² (A)