In a parallelogram, one of the sides is 10 cm, one of the corners is 30 °. Find the area of the parallelogram

univerkov | September 17, 2021 | education

In a parallelogram, one of the sides is 10 cm, one of the corners is 30 °. Find the area of the parallelogram if its perimeter is 56 cm.

1. Let us denote the vertices of the parallelogram by the symbols A, B, C, D. Angle A is equal to 30 °. AB = 10 cm.

2. Draw the height BH to the AD side.

3. Calculate its length through the sine of angle A:

BH: AB = sine of angle A = sine 30 ° = 1/2.

BH = 10 x 1/2 = 5 cm.

4. Calculate the length of the side AD, using the formula for calculating the perimeter of a parallelogram:

2 (AB + AD) = 56 cm.

AB + AD = 28 cm.

AD = 28 – AB = 28 – 10 = 18 cm.

5. Area of the parallelogram = AD x BB = 18 x 5 = 90 cm ^ 2.

Answer: the area of the parallelogram ABCD is 90 cm ^ 2.

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