A parallelogram and a rectangle have the same side. Find the area of a parallelogram if the acute angle is 30 ° and the area of the rectangle is 26.
1. A, B, C, D – the tops of the parallelogram. M, N, K, P – the vertices of the rectangle. ∠А = 30 °.
S – area.
2. According to the condition of the problem, the sides of both geometric figures are equal, that is, AB = MN, AD = MР.
3. S rectangle = МN х МР = 26 cm². Therefore AB x AD = 26 cm².
4. From the vertex B of the parallelogram, draw the height HВ. In a right-angled triangle ABN, it is a leg opposite an angle of 30 °.
Therefore, BH = 1/2 AB.
5. S parallelogram = AD x BH = AD x AB / 2 = 26: 2 = 13 cm².
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