Question

The given figure consists of a triangle, a circle and a square. All three shapes have the same area. The ratio of the unshaded area of the triangle to the whole area of the triangle is 5:8. Half of the circle is unshaded. If fraction of the whole figure that is unshaded can be written in the form p/q, where p and q are coprime then, find the value of p + q.

Answer 1

Heyy Bro !!
Here is your answer!!

Final Result : p/q = 5/12
i.e., p+ q = 5+12=17.

According to the question,
A(Circle) = A(Square)=A(Triangle)=A(say)5A/8

Let
A(C1) = >Shaded area of Circle.
A(C2) = >Unshaded area of Circle.
A(S1) = >Shaded area of rectangle .
A(S2) = >Unshaded area of rectangle
A(T1) = >Shaded area of Triangle.
A(T2) => Unshaded Area of Triangle.

Then,
According to the question, we get

A(T2)/A(Triangle) = 5/8
=>A(T2) = 5A/8. ----------(1)
=>A(T1) = A- 5A/8 = 3A/8 -----------(1')

A(C2)/A(Circle) = 1/2
=>A(C2) = A/2. --------(2)
=>A(C1) = A-A/2 = A/2 ----(2')

Now,
By looking at figure , we can say that

A(C1) =A(S1) + A(T1)
=> A/2 = A(S1) + 3A/8
=> A/2 -3A/8 = A(S1) (By eq. (1') & eq.(2'))
=> A(S1) = A/8. ----(3)

Then,
Fraction of unshaded figure =
[ A(C2) + A(T2) + A(S2) ] / [ A +A+ A]

By using eq. (1),(2),(3),
=> (A /2 + 5A/8 + A/8 )/ 3A =( 10A/4) / 3
= 5/12



Hope, you understand answer and it may helps you!!