Given an isosceles triangle with a base of 80 cm and an angle of 45. Find the area.

Let ΔABC – isosceles triangle, AB = BC, AC = 80 cm – base, A = 45 °.

Then A = C = 45 °. Let’s calculate the value of the angle B: B = 180 – A – C = 180 – 45 – 45 = 90 °.

ΔАВС – right triangle, АС – hypotenuse. We calculate the length of the legs, taking into account that AB = BC:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AC ^ 2 = 2 * AB ^ 2;

AB ^ 2 = 6400/2;

AB = √3200 = 10√2 cm.

BC = 10√2 cm.

SΔABS = (1/2) * AB * BC – the area of a right-angled triangle is equal to half the product of the legs:

SΔАВС = (1/2) * 10√2 * 10√2 = 1600 cm2.

Answer: 1600 cm2.