In a right-angled triangle ABC AB = 6 cm, AC = 10 cm. Points F and T are the midpoints of sides AB and BC, respectively. Calculate the area of the triangle BFT.
By the Pythagorean theorem, we find the second leg BC:
ВС = √ (AC² – AB²) = 8 (cm).
We find the area of the triangle ABC:
S ABC = 1/2 * AB * BC = 1/2 * 6 * 8 = 24 (cm²).
Triangles ABC and BFT are similar, the coefficient of similarity is 1/2.
S BFT = S ABC * k² = 24 * 1/4 = 6 (cm²).
Answer: The area of the triangle BFT is 6 cm².
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