Doubling the Area of a Square by Construction

Q.

Find the areas of the squares whose sides is : $14cm$

Q.

Two lines are drawn parallel to the diagonal of a square as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square of the area $61c{m}^2$ as shown in the second figure, then the area of the original square is

1. $61c{m}^2$

2. $30c{m}^2$

3. $30.5c{m}^2$

4. $122c{m}^2$

Q.

Find the areas of the squares whose sides are: $5cm$

Q.

Find the areas of the squares whose sides are: $10cm$.

Q.

Two lines are drawn parallel to the diagonal of a square as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square of the area $100c{m}^2$ as shown in the second figure, then find the area of the original square.

1. $75c{m}^2$

2. $25c{m}^2$

3. $100c{m}^2$

4. $50c{m}^2$

Q.

Two lines are drawn parallel to the diagonal of a square as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square, then the area of the larger square is ____.

1. Same as the area of the original square

2. Half the area of the original square

3. Double the area of the original square

4. 3 times the area of the original square

Q.

Each diagonal of a square is $12cm$ long. Its area is
(a) $144c{m}^2$
(b) $72c{m}^2$
(c) $36c{m}^2$
(d) none of these

Q. What is the length of the bigger square formed by joining four squares of length 3 cm?​

1. 5 cm
2. 6 cm
3. 4 cm
4. 8 cm

Q.

The length of a side of a square field is $4m$. What will be the altitude of the rhombus, if the area of the rhombus is equal to the square field and one of its diagonals is $2m$?

Q.

Four corners of a square are folded as shown in the first two figures. It is unfolded and cut along the creases to get a new square of the area $14.5c{m}^2$. The area of the original square is _____.

1. $14.5c{m}^2$

2. $29c{m}^2$

3. $43.5c{m}^2$

4. $7.25c{m}^2$

Q. Given a square ABCD of side 10 M and another quadrilateral is formed by joining midpoints of all side of the given figure.If the area of square ABCD =(R) area of EFGH.Then find the value of k what can be said about the quadrilateral EFGH?

Q.

How about a square of area 41 square centimeters?

Q.

Two lines are drawn parallel to the diagonal of a square of area $25c{m}^2$ as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square as shown in the second figure, then the area of the larger square is _____.

1. $50c{m}^2$

2. $25c{m}^2$

3. $12.5c{m}^2$

4. $75c{m}^2$

Q.

A rectangular field has an area of $1,764m^2$.

The width of the field is $13m$ more than the length.

What is the perimeter of the field?

Q. Each diagonal of a square is 12 cm long. Its area is

(a) 144 cm²
(b) 72 cm²
(c) 36 cm²
(d) none of these

Q. Two squares of same size are joined together to make a single square of area 32 sq.cm. Find the length of each side of the small square.

Q.

Two lines are drawn parallel to the diagonal of a square as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square of the area $61c{m}^2$ as shown in the second figure, then the area of the original square is

Q. Three squares of identical side lengths are combined to form a large square of area 192 sq. cm. Determine the side length of the smaller squares.

Q.

How do we draw a square of area 8 square centimeters?

Q.

Two small squares are joined to make a larger square of area 32 Sq.cm. The area of the each small square is _____.

1. 9 sq.cm

2. 4 sq.cm

3. 25 sq.cm

4. 16 sq.cm

Q.

A square is cut along its diagonal to form four triangles and these are arranged on another square of same area to form a larger square. The area of the larger square is 64 sq.units. Then find the area of the original square.

$\left[2\right]$

Q. Find the area of a square, the length of whose diagonal is 64 cm.

Q.

Two lines are drawn parallel to the diagonal of a square of area $17c{m}^2$ as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square as shown in the second figure, then the area of the larger square is

1. $34c{m}^2$

2. $32c{m}^2$

3. $8.5c{m}^2$

4. $51c{m}^2$

Q.

Find the rate of change of the area of a square with respect to the length $z$, the diagonal of the square. what is the rate when $z=2$?

Q.

Now can’t we draw a square of area 20 square centimeters?

Q. Given a square ABCD of side 10 M and another quadrilateral is formed by joining midpoints of all side of the given figure.If the area of square ABCD =(R) area of EFGH.Then find the value of k what can be said about the quadrilateral EFGH?

Q. Two lines are drawn parallel to the diagonal of a square as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square of the area $100c{m}^2$ as shown in the second figure, then the area of the original square is ___.

1. 50

Q. the area of a square ABCD is 36 m². find the area of the square obtained by joining the midpoints of the sides of the square ABCD.

Q. A square can be enlarged into a bigger square using concept of parallel lines.

1. True
2. False

Q.

If the sides of a square are halved, then its area

1. remains same

2. becomes half

3. becomes one-fourth

4. $doubles$