A rhombus is a parallelogram, all sides of which are equal. It is known from the properties of the rhombus that the diagonals are halved by the intersection point and intersect at right angles.
The length of the diagonal is known, we find its half:
d1 = D1 / 2 = 80/2 = 40 (conventional units)
The diagonals at the intersection form 4 identical right-angled triangles. Consider one of these triangles.
In a triangle, the leg (half of the known diagonal) and the hypotenuse (side of the rhombus) are known, we find the second leg (half of the unknown diagonal) by the Pythagorean theorem:
K1 ^ 2 + K2 ^ 2 = T ^ 2;
40 ^ 2 + K2 ^ 2 = 50 ^ 2;
K2 ^ 2 = 2500 – 1600;
K2 ^ 2 = 900;
К2 = √900 = 30 (conventional units).
The second unknown diagonal of the rhombus will be:
D2 = K2 * 2 = 30 * 2 = 60 (conventional units).
The area of the rhombus is found by the formula:
S = (D1 * D2) / 2
S = (80 * 60) / 2 = 2400 (conventional units squared).
Answer: 2400 conventional units squared.
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