The side of the rhombus is 20 cm, one diagonal is 32 cm, find the area and perimeter.

univerkov | August 8, 2021 | education

1. The vertices of the rhombus A, B, C, D. O – the point of intersection of the diagonals. Diagonal AC = 32 cm. S – area. P is the perimeter.

2. The AC diagonal divides the rhombus into two equal triangles: ABC and ACD. The area of each of them is equal to 1/2 the area of the rhombus.

3. S triangle ACD = AC x OD / 2.

OD = √AD² – AO² (by the Pythagorean theorem). AO = 1/2 AC = 16 centimeters. AD = 20 cm.

OD = √20² – 16² = √400 – 256 = √144 = 12 cm.

S triangle АСD = 32 х 12/2 = 192 cm².

4. S rhombus = 192 x 2 = 384 cm².

5.R = 20 x 4 = 80 cm.

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