The area of a rectangle is equal to the product of its length and width:
S = a b.
The diagonal of the rectangle AC divides it into two right-angled triangles. Consider one of them, the ABC triangle. Suppose the angle ∠C is 36 °.
With the help of the cosine tower, you can find the length of the BC side:
cos C = BC / AC;
BC = AC · cos C;
cos 36 ° = 0.809;
BC = 10 0.809 = 8.09 cm.
Behind the sine theorem, you can find the length of the side AB:
sin C = AB / AC;
AB = AC sin C;
sin 36 ° = 0.588;
AB = 10 0.588 = 5.88 cm.
Now let’s find the area of the rectangle:
S = 8.09 5.88 = 47.57 cm2.
Answer: the area of the rectangle is 47.57 cm2.
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