Question

What is the area of the colored square..please find the image attached. Need the explanation..Looks like sekharu posted a same question yesterday but I cannot find the explanation.

Answer 1

First, we find the area of the big square, as all its sides are equal to 15 units (10+5 units)

∴ area of big square = (side)² = 15×15 units² = 225 units²

Now, on seeing the blue square, it will be noticed that the unshaded portion is equivalent to four separate right-angled triangles, having the same dimensions.

Each of these right-angled triangles consist of;

base = 5 units

perpendicular = 15 units

∴ area of 1 right-angled triangle =  $\frac{base*perpendicular}{2}$ units²

= $\frac{5*15}{2}$ units² = $\frac{75}{2}$ units² = 37.5 units²

∴ area of unshaded region = 4 × (area of one right-angled triangle) = (4 × 37.5) units² = 150 units²

∴ area of blue square = (area of big square) - (area of unshaded region) = (225-150) units² = 75 units²

Ans) Area of the coloured square = 75 units²

Answer 2

90 sq. unit.

Step-by-step explanation:

Area of the outer square with length of side 10+5 = 15² = 225 sq. unit.

Now finding the area of triangle of base 5 unit and height = 1 / 2 × 5 × 15 = 75 / 2 = 37.5 sq. unit.

There are four similar triangles in the given square so total area of all four is : = 4 × 75 / 2 = 150 sq. unit.

To get the colored square area we need to find the area of four small triangles as well and subtract them from the area of big triangles.

The height of a right triangle of perpendicular sides p and q and

hypotenuse x, which is perpendicular to y, is,  

x = p q  / y :

where, x = 1.5 unit

then, Area of small triangle = 4 × 1 / 2 × 1.5 × 5 sq. unit

Area of 4 small triangles = 15 sq. unit.

= > 150 - 15 = 135 sq. unit.

Area of big square - 135 sq. unit.

Then Area of coloured square = 225 - 135 sq. unit

= Area of colored square = 90 sq. unit.