The perimeter of a rectangle is 14 8 15 cm . If its length is 4 2 3 cm , find its area.

Given length of a rectangle l = 4 2 3 cm Let the breadth of the rectangle is b cm . We know that perimeter of the rectangle is 2 l + b Given perimeter of the rectangle is 14 8 15 cm . ⇒ 2 l + b = 14 8 15 ⇒ 2 4 2 3 + b = 14 8 15 ⇒ 2 4 × 3 + 2 3 + b = 14 × 15 + 8 15 ⇒ 2 12 + 2 3 + b = 210 + 8 15 ⇒ 2 14 3 + b = 218 15 ⇒ 14 3 + b = 218 5 × 1 2 ⇒ b = 218 30 - 14 3 ⇒ b = 218 - 140 30 ⇒ b = 78 30 ⇒ b = 13 5 = 2 3 5 cm We know that area of the rectangle is l × b . ⇒ 4 2 3 × 13 5 ⇒ 4 × 3 + 2 3 × 13 5 ⇒ 14 3 × 13 5 ⇒ 182 15 cm 2 = 12 2 15 cm 2 Hence, the area of the rectangle is 12 2 15 cm 2

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Find the area of the square with the given side.

$43 cm$

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Important Questions on Measurements and Units

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Science>Physics>Measurements and Units>Area, Volume and Density

In the following figure, $seg DH ⊥ seg EF$ and $seg GK ⊥ seg EF$ . If $DH = 6 cm, GK = 10 cm$ and $A (△ DEF) = 150 {cm}^{2}$ , then find $A (△ GEF)$ in ${cm}^{2}$ .

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Science>Physics>Measurements and Units>Area, Volume and Density

A square park is of side

100 m

. A road

5 m

wide is made all around the garden inside it. If the area of the road is

r m^{2}

, then find the value of

r

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Science>Physics>Measurements and Units>Area, Volume and Density

In the following figure, $seg DH ⊥ seg EF$ and $seg GK ⊥ seg EF$ . If $DH = 6 cm, GK = 10 cm$ and $A (△ DEF) = 150 {cm}^{2}$ , then find $EF$ in $cm$ .

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Science>Physics>Measurements and Units>Area, Volume and Density

A B C

is an equilateral triangle of side

2 a

. Find each its altitudes.

EASY

Science>Physics>Measurements and Units>Area, Volume and Density

A wire encloses an area of

616 {cm}^{2}

when it is bent in the form of a circle. If the wire is bent in the form of a square, then its area (in

{cm}^{2}

) is very nearly equal to: (Take

π = \frac{22}{7}

)

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Science>Physics>Measurements and Units>Area, Volume and Density

From a rectangular piece of metal sheet of length and breadth

1 \cdot 60 m and 80 cm

respectively,

3

circular sheets of

20 cm

radius are cut out. If the area of metal left is

A m^{2}

, then what is the value of

A

(Use : π = \frac{22}{7})

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Science>Physics>Measurements and Units>Area, Volume and Density

The perimeter of a rectangle is

14 \frac{8}{15} cm

. If its length is

4 \frac{2}{3} cm

, find its area.

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Science>Physics>Measurements and Units>Area, Volume and Density

A Square copper plate of side

16 cm

weighs

128 gm

. A circular disc of diameter

14 cm

is cut off from the plate. What is the weight of remaining part ?

(π = \frac{22}{7})

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Science>Physics>Measurements and Units>Area, Volume and Density

Side of a square is first increased by

10 %

and then decreased by

20 %

. What is the overall percentage change in area?

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Science>Physics>Measurements and Units>Area, Volume and Density

Find the area of rectangle, whose length is

7 cm

and breadth is

3.5 cm

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Science>Physics>Measurements and Units>Area, Volume and Density

A wire is bent to form a square of area $169 \mathrm{~cm}^{2}$. If the same wire is bent to form a circle, then what is its area (in $\mathrm{cm}^{2}$, to the nearest whole number)?
Take $\pi=\frac{22}{7}$

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Science>Physics>Measurements and Units>Area, Volume and Density

What is the area of the largest square which can be inscribed in a circle of radius

28 cm ?

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Science>Physics>Measurements and Units>Area, Volume and Density

The area of a square shaped field is

1764 m^{2}

. The breadth of a rectangular park is

\frac{1}{6} th

of the side of the square field and the length is four times its breadth. What is the cost (in ₹) of levelling the park at

₹ 30 per m^{2}

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Science>Physics>Measurements and Units>Area, Volume and Density

A rectangular plot is

40 m

long and

16 m

broad. A path of uniform width of

2 m

surrounded the plot inside it. Find the cost of paving the road with bricks at

₨ 15

per square meter and also the cost of covering the remaining part of the plot with grass at

₨ 9

per square meter.

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Science>Physics>Measurements and Units>Area, Volume and Density

If the area of a square is $2401 x^{4} + 196 x^{2} + 4$ , then what is its side length?

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Science>Physics>Measurements and Units>Area, Volume and Density

The area of a square if its perimeter is

64 cm

A {cm}^{2}

. Find the value of

A

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Science>Physics>Measurements and Units>Area, Volume and Density

What is the area of the largest square which can be inscribed in a circle of radius

14 cm ?

(Take

π = \frac{22}{7}

)

EASY

Science>Physics>Measurements and Units>Area, Volume and Density

The area of a right angled triangle having base

24

cm

and hypotenuse

25

cm

is_____.

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Science>Physics>Measurements and Units>Area, Volume and Density

The radius of a circle is twice the side of a square, whose area is

196 m^{2}

. The length of the rectangle is twice the diameter of the circle. What is the perimeter of a rectangle if its breadth is half the length?

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Science>Physics>Measurements and Units>Area, Volume and Density

A poster of size

10 cm

8 cm

is pasted on a sheet of cardboard such that there is a margin of width

1.75 cm

along each side of the poster. Find the total area of the margin and the cost of the cardboard used at the rate of

₹ 0.60 p e r {cm}^{2}

Find the area of the square with the given side. 43 cm

Important Questions on Measurements and Units

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Find the area of the square with the given side.

$43 cm$