The height BD of triangle ABC divides the base AC into segments: AD = 8cm

univerkov | July 21, 2021 | education

The height BD of triangle ABC divides the base AC into segments: AD = 8cm BC = 12cm, and the angle A at the base is 45 degrees. Find the area of this triangle.

Triangle ABD – rectangular (ВD – height, <ADB = 90 °).

<ABD = 180 ° – <A – <ADB = 180 ° – 45 ° – 90 ° = 45 °;

<A = <ABD = 45 °, therefore, ΔABD is isosceles:

AD = BD = 8 cm;

AC = AD + DC = 8 cm + 12 cm = 20 cm;

SABD = (AC * BD) / 2 = (20cm * 8cm) / 2 = 80cm ^ 2.

Answer: 80 cm ^ 2.

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