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) = (opposite)/(adjacent)`

Where,

`tan(\theta) = tan(60) = √(3)`

Opposite = BD

Adjacent = 7 cm

Plug in the values

`√(3) = (BD)/(7)`

Multiply both sides by 7

`7√(3) = BD`

`BD = 7√(3)`

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

Thus:

`tan(\theta) = (opposite)/(adjacent)`

Where,

`tan(\theta) = tan(60) = √(3)`

Opposite = 6 cm

Adjacent = BF

Plug in the values

`√(3) = (6)/(BF)`

`BF = (6)/(√(3))`

Rationalize

`BF = (6 * √(3))/(√(3) * √(3))`

`BF = (6√(3))/(3)`

`BF = 2√(3)`

✔️Perimeter of rectangle BDEF:

Perimeter = 2(BD + BF)

Plug in the values

`Perimeter = 2(7√(3) + 2√(3))`

`Perimeter = 2(9√(3))`

`Perimeter = 18√(3)`

✔️Area of the rectangle BDEF:

Area = BD × BF

Plug in the values

`Area = 7√(3) * 2√(3)`

`Area = 7 * 2√(3 * 3)`

`Area = 14 * 3`

`Area = 42`