The diagonals of the trapezoid divide it into four triangles. The areas of three of them are equal to 4
| May 25, 2021 | education
The diagonals of the trapezoid divide it into four triangles. The areas of three of them are equal to 4, 6 and 9. Find the area of the fourth.
By the property of the diagonals of a trapezoid, they divide it into four triangles, two of which, belonging to the lateral sides, are equal in size. Savo = Ssvo, S1 = S3.
Also, the product of the areas formed at the bases is equal to the product of the areas of the triangles formed at the lateral sides S2 * S4 = S1 * S3 = S1 ^ 2.
Then S1 = 9 cm2, S2 = 4 cm2, S4 = 9 cm2.
4 * 9 = 6 * H.
X = S3 = 36/6 = 6 cm2.
Answer: The area of the triangle is 6 cm2.
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