The diagonal of the parallelogram divides it into two triangles, the area of one of which
| April 19, 2021 | education
The diagonal of the parallelogram divides it into two triangles, the area of one of which is 14 cm2. What is the area of the parallelogram?
Consider triangles ABC and BCD.
Since the opposite sides of parallelograms are equal, AB = CD, BC = AD. The triangles have a common side BD. Therefore, triangles ABD and BCD are equal on three sides, according to the third attribute.
In equal triangles, the areas are equal, then Savd = Svsd, and the area of the parallelogram is equal to twice the area of the triangle ABD.
Savd = 2 * Savd = 2 * 14 = 28 cm2.
Answer: The area of the parallelogram is 28 cm2.
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