Question

Calculate the area

Answer 1

`\huge \boxed{\mathrm{35.64 \ units^2 }}`

Explanation:

The adjacent side lengths and an angle is given.

We need to find the height of the parallelogram.

A small right triangle is formed with an angle of 63 degrees and an hypotenuse of 5 units.

We can use trigonometric functions to solve for the height.

sin θ = opp/hyp

sin 63 = h/5

Multiplying both sides by 5.

h = 5 sin 63

h ≈ 4.45503262

Area of parallelogram = base × height

A = 8 × 4.45503262

A = 35.640261

Answer 2

`A=a\cdot b\cdot \sin\angle AB\\\\A=5\cdot8\cdot\sin63^\circ\\\\A=40\cdot0.891\\\\\boxed{A=35.64}`