Question

Abc is a Isoceles right angled triangle and pqrs is a Rectangle... Find the area of shaded region

Answer 1

In triangle APQ,
Angle APQ + Angle AQP + Angle PAQ = 180 & Angle APQ = Angle AQP

In triangle ABC,
Angle ABC + Angle BCA + Angle CAB = 180 & Angle ABC = Angle BCA

Due to Similar angles on two parallel lines, Angle ABC = Angle APQ & Angle PAQ = Angle CAB due to Similar angle

In triangle BPS, which is a rt angle triangle
Angle PBS + Angle BSP + Angle SPB = 180 & Angle PBS = Angle ABC similar angles

Angle PBS = 90 - Angle ABC

Since straight line is formed by points BPA,
Angle PBS + 90 + Angle APQ = 180

Use the above equations to solve and get the value of angle. Then using sin or cos functions get the value of length BS and length PS. The dimensions of rectangle can be used to calculate the area which can be subtracted from area of triangle ABC