In trapezium ABCD, the diagonals AC and BD are drawn. The area of the triangle ABD is 57 cm2.
| September 1, 2021 | education
In trapezium ABCD, the diagonals AC and BD are drawn. The area of the triangle ABD is 57 cm2. Determine the area of the triangle ACD.
Let’s draw the height BH and CK of the trapezoid ABCD.
Consider triangles ABD and ACD.
The area of the triangle ABD is equal to: Savd = AD * BH / 2 = 57 cm2.
The area of the triangle ACD is equal to: Sacd = AD * CK / 2.
Since the height CK = BH, then Sacd = AD * BH / 2 = Savd = 57 cm2.
Answer: The area of the ACD triangle is 57 cm2.
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