How to find the area of a parallelogram knowing that the diagonals are 8 cm and the height is 6?

To solve this problem, consider a right-angled triangle formed by the diagonal, height and width of this parallelogram;

For ease of writing and explanation, we introduce the following designations;

L = 8cm – diagonal;

H = 6cm – height;

X – length;

Let’s use the Pythagorean theorem;

D2 = H2 + X2;

X2 = D2 – H2;

X = √ (82 – 62);

X = √ (64 – 36);

X = √28 = 2√7;

Knowing two legs, we can find the area of a given triangle, then the entire area of the parallelogram will be equal to two areas of the triangles;

S = 2 * St = 2 * (1/2 * 6 * 2√7) = 12√7cm2.