Question

I'm very confused, I don't know where to even start! Please help me!!

Answer 1

Answer/Step-by-step explanation:

✔️Using trigonometric ratio, find width of the rectangle, BD:

Thus:

$tan(\theta) = \frac{opposite}{adjacent}$

Where,

$tan(\theta) = tan(60) = \sqrt{3}$

Opposite = BD

Adjacent = 7 cm

Plug in the values

$\sqrt{3} = \frac{BD}{7}$

Multiply both sides by 7

$7\sqrt{3} = BD$

$BD = 7\sqrt{3}$

✔️Using trigonometric ratio, find height of the rectangle, BF:

Thus:

$tan(\theta) = \frac{opposite}{adjacent}$

Where,

$tan(\theta) = tan(60) = \sqrt{3}$

Opposite = 6 cm

Adjacent = BF

Plug in the values

$\sqrt{3} = \frac{6}{BF}$

$BF = \frac{6}{\sqrt{3}}$

Rationalize

$BF = \frac{6 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

$BF = \frac{6\sqrt{3}}{3}$

$BF = 2\sqrt{3}$

✔️Perimeter of rectangle BDEF:

Perimeter = 2(BD + BF)

Plug in the values

$Perimeter = 2(7\sqrt{3} + 2\sqrt{3})$

$Perimeter = 2(9\sqrt{3})$

$Perimeter = 18\sqrt{3}$

✔️Area of the rectangle BDEF:

Area = BD × BF

Plug in the values

$Area = 7\sqrt{3} \times 2\sqrt{3}$

$Area = 7 \times 2\sqrt{3 \times 3}$

$Area = 14 \times 3$

$Area = 42$