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

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

Determine the length BD from a right-angled triangle ABD using the definition of the tangent of an angle:
tg BAD = BD / AD;
BD = tan BAD * AD = tan 45 ° * 8 = 1 * 8 = 8 cm.

Find the length of the base of triangle ABC:
AC = AD + DC = 8 + 12 = 20 cm.

Let’s calculate the area of the triangle:
S abc = 1/2 * a * h = 0.5 * AC * BD = 0.5 * 20 * 8 = 80 cm².

Answer: The area of a given triangle is 80 square centimeters.