ABCD-rhombus, angle A = 30 degrees, rhombus height 10 cm. Find Area (S).

univerkov | May 7, 2021 | education

Let ABCD be the given rhombus, DH the height.

Consider the DHA triangle.

This triangle is rectangular because ∠DHA = 90 ° (DH – height).

In a right-angled triangle, the leg, opposite an angle of 30 °, is equal to half the hypotenuse.

DH = ½ DA, DA = 2DH = 2 * 10 = 20 (cm).

Because in a rhombus, all sides are equal, then AB = DA = 20 cm.

Area of triangle АDB SADB = ½ AB * DH = ½ * 20 * 10 = 100 (sq. Cm).

Area of a rhombus S = 2SADB = 2 * 100 = 200 (sq. Cm).

Answer: S = 200 (sq. Cm).

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