Answer: Area of shaded part is 50 cm².
Step-by-step explanation:
Since we have given that
Ratio of height of triangle to side length of the square is 7:8.
Let height of triangle be 'h'.
Let the length of square be 'a'.
Let the base of triangle be 'b'.
Ratio of base of triangle to side length of the square is 1:2.
So, Combined ratio will be
h : a : b
7 : 8
4(2 : 1) (to make 'a' as a common part which is 8 )
= 8 : 4
----------------------------------
7 : 8 : 4
So, height will be 7x.
Side will be 8x.
Base will be 4x.
Since area of square = 64 cm²
As we know that "Area of square = Side × Side":
[tex]64=(8x)^2\\\\64=64x^2\\\\x^2=1\\\\x=1(\text{negative value will be discarded})[/tex]
So, base becomes 4 inches.
Height becomes 7 inches.
So, Area of triangle becomes
[tex]Area=\frac{1}{2}\times base\times height\\\\Area=\frac{1}{2}\times 7\times 4\\\\Area=2\times 7\\\\Area=14\ cm^2[/tex]
Area of shaded part of the square is
Area of square - Area of triangle
[tex]=64-14\\\\=50\ cm^2[/tex]
Hence, Area of shaded part is 50 cm².
