# In a right-angled triangle ABC, angle C = 90 degrees, point D divides the AC side into segments AD

September 23, 2021 | education

| **In a right-angled triangle ABC, angle C = 90 degrees, point D divides the AC side into segments AD = 9 cm and CD = 4 cm. Triangle area = 91 cm square. Find the area of the ABD triangle.**

Determine the length of the AC leg.

AC = AD + CD = 9 + 4 = 13 cm.

Let’s apply the formula for the area of a triangle.

Savs = AB * AC / 2.

91 = AB * 13/2.

AB = 91 * 2/13 = 14 cm.

Determine the area of the triangle ABD.

Savd = AB * AD / 2 = 14 * 9/2 = 63 cm2.

Answer: The area of triangle ABD is 63 cm2.

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