The diagonals of the quadrilateral ABCD, intersect at right angles, are halved.
| May 7, 2021 | education
The diagonals of the quadrilateral ABCD, intersect at right angles, are halved. The lengths of the diagonals are 6 cm and 8 cm. How to calculate the area of a quadrilateral ABCD.
1. The sign of a rhombus is known: if the diagonals of a quadrangle are mutually perpendicular, then it is a rhombus.
2. By the condition of the problem, the diagonals of the quadrilateral intersect at right angles, which means ABCD is a rhombus.
It is known that the area of a rhombus is half the product of its diagonals.
We calculate the area S of a rhombus if the lengths of its diagonals are 8 centimeters and 6 centimeters.
S = 8 cm * 6 cm: 2 = 48 cm ^ 2: 2 = 24 cm ^ 2.
Answer: The area of a quadrangle is 24 square centimeters.
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