The side of the rhombus is 26 cm and one of the diagonals is 48 cm. Find the area of the rhombus.

univerkov | April 8, 2021 | education

1. Note that the diagonal divides the rhombus into two equal triangles. In our case, into two triangles with sides, the lengths of which are 26 cm, 26 cm and 48 cm.

2. Find the area of such a triangle. For this we will use Heron’s formula:
S ^ 2 = p * (p – a) * (p – b) * (p – c). In this formula, S is the area of the triangle; a, b and c – the lengths of the sides of the triangle; p = (a + b + c) / 2.

3. Substitute the values of the sides of the triangle in the formula. We get:
S ^ 2 = 50 * (50 – 26) * (50 – 26) * (50 – 48) = 50 * 24 * 24 * 2 = 100 * 24 * 24.

4. Extract the square root. We get: S = 10 * 24 = 240 sq. cm.

5. We have calculated the area of a triangle, which is half a rhombus. Therefore, the area of the entire rhombus is: 240 * 2 = 480 sq. cm.

Answer: the area of the rhombus is 480 sq. cm.

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