Given: BD perpendicular to AC; angle C = 45 °; AD = 6cm, CD = 4cm. Find the area of a triangle ABC.

Since BD is perpendicular to AC, triangle BCD is right-angled. If in this triangle <C = 45, then <DBC = 180 – (90 + 45) = 45. So triangle BCD is also isosceles, in which BC is the base, and BD and DC are the sides. In an isosceles triangle, the sides are equal.

BD = CD = 4 cm.

For a triangle ABC, BD is the height, AC is the base.

AC = AD + DC;

AC = 6 + 4 = 10 (cm)

S tr. = 1/2 * ah, a = AC, h = BD;

S tr. = 1/2 * 10 * 4 = 40/2 = 20 (cm ^ 2).

Answer. 20 cm ^ 2.