Find the area of a triangle ABC with vertices A (-4; 0) B (3; 8) C (2;).

univerkov | February 28, 2021 | education

Determining the area by Heron’s theorem is not convenient, since the lengths of the segments are not integers.

From the vertices B and C, construct the perpendiculars BD and CH to the OX axis.

ВD = 8 cm, AD = (4 + 3) = 7 cm, then Savd = 8 * 7/2 = 28 cm.

Ssn = AН * CH / 2 = 6 * 2/2 = 6 cm2.

Quadrangle НСВD is a rectangular trapezoid, then Sнсвд = (2 + 8) * 1/2 = 5 cm2.

Then Savs = 28 – 6 – 5 = 17 cm2.

Answer: The area of the triangle is 17 cm2.

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