Question

The area of the largest square in the figure is 144 sq. units. What
is the area of shaded square if the corners of each square lie on
the midpoint of the sides of the next larger square?
a) 14
b) 16
c) 18
d) 20​

Answer 1

your answer is here

C )18 because

$144 \div 8 (2 \times 4)$

$<marquee>☺☺Please Mark As The Brainliest Answer ☺☺$

Answer 2

Therefore the area of the shaded area is 18 sq units. ( Option-c )

Given:

The area of the largest square in the figure = 144 sq units

All the squares lie on the midpoint of the larger square.

To Find:

The area of the shaded square.

Solution:

The given question can be answered as shown below.

The area of the largest square in the figure = 144 sq units

Largest square:

Area of the square = a² = 144

So the length of the side of the largest square a = √ 144 = 12 units.

Second largest square inside the first square of side 12 units:

The vertices of the second largest square lie at midpoints ( 6 units ) of the largest square.

So half lengths of the largest square and the side of the second largest square from right angle isosceles triangle.

Hence Pythagoras Theorem:

Length of the side of second largest square b = √ 6² + 6² = 6√2 units

Square inside the second largest square of side 6√2 units:

The vertices of the third largest square lie at midpoints ( 3√2 units ) of the second largest square.

So half lengths of the second largest square and the side of the third largest square from right angle isosceles triangle.

Hence Pythagoras Theorem:

Length of the side of third largest square c = √ ( 3√2 )² + ( 3√2 )² = √ 18 + 18 = √36 = 6 units

The shaded square which is inside the third largest square of side 6 units:

The vertices of the shaded square lie at midpoints ( 3 units ) of the third largest square.

So half lengths of the third largest square and the side of the shaded square from right angle isosceles triangle.

Hence Pythagoras Theorem:

Length of the side of shaded square d= √ ( 3² + 3² ) = √ 9 + 9 = √18 = 3√2 units

Hence the area of the shaded square = d² = ( 3√2 )² = 9 × 2 =18

Therefore the area of the shaded area is 18 sq units.

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