Mensuration

If the length and breadth of a rectangle are $10$ m and $5$ m respectively, find its area.

Find the perimeter of a rectangle whose area is $600$ cm$^2$ and breadth is $20$ cm.

The area of a square is $1$ hectare. What is its side in meters?

A wire of length $40$ cm is bent into a square. Find the side of the square.

The ratio of length to breadth of a rectangle is $5:3$. If the area is $375$ cm$^2$, find its perimeter.

If the side of a square is increased by $10\%$, by what percentage does its area increase?

A path $1$ m wide is built inside a rectangular park of length $30$ m and breadth $20$ m. Find the area of the path.

If the side of a square is increased by $20\%$, what is the percentage increase in its area?

A marble tile measures $20\text{ cm} \times 25\text{ cm}$. How many such tiles will be required to cover a wall of size $4\text{ m} \times 3\text{ m}$?

The perimeter of a rectangular sheet is $100\text{ cm}$. If the length is $35\text{ cm}$, find its area.

Find the area of the given shape, which is a parallelogram with a base of $20\text{ cm}$ and a perpendicular height of $15\text{ cm}$.

Calculate the area of a triangle whose sides are $3\text{ cm}$, $4\text{ cm}$ and $5\text{ cm}$.

A triangle has an area of $28\text{ cm}^2$ and a base of $7\text{ cm}$. Find its height.

In the given parallelogram, if the area is $120\text{ cm}^2$ and the height is $10\text{ cm}$, find the base.

In the figure, $ABCD$ is a parallelogram. $P$ is a point on $DC$. If the area of triangle $ABP$ is $25\text{ cm}^2$, find the area of the parallelogram $ABCD$.

A field is in the shape of a parallelogram with base $40\text{ m}$ and height $25\text{ m}$. Find the cost of leveling it at Rs 5 per square meter.

The ratio of the base and height of a triangle is $3:2$. If the area is $108\text{ cm}^2$, find the base.

A rhombus has a perimeter of $52$ cm and one of its diagonals is $24$ cm. Find the area of the rhombus.

In the given figure, $ABCD$ is a rectangle with $AB = 20$ cm and $BC = 10$ cm. $E$ is the midpoint of $DC$. Calculate the area of the triangle $ABE$.

Two adjacent sides of a parallelogram are $24$ cm and $18$ cm. If the distance between the longer sides is $12$ cm, find the distance between the shorter sides.

A rhombus has a side of $13\text{ cm}$ and an area of $156\text{ cm}^2$. What is its altitude?

If the area of a rhombus is $80\text{ cm}^2$ and one diagonal is $16\text{ cm}$, find the length of the other diagonal.

Find the area of a rhombus whose side is $6.5\text{ cm}$ and altitude is $4\text{ cm}$.

Calculate the area of a rhombus whose side is $12\text{ cm}$ and the perpendicular distance from the opposite vertex to the side is $7\text{ cm}$.

In the given figure, $ABCD$ is a rhombus where the diagonals $AC$ and $BD$ intersect at point $O$. If the length of diagonal $AC = 16\text{ cm}$ and the length of diagonal $BD = 12\text{ cm}$, calculate the area of the rhombus.

The diagonals of a rhombus are $16\text{ cm}$ and $30\text{ cm}$. Find its perimeter.

Each side of a rhombus is $15\text{ cm}$ and one of its diagonals is $24\text{ cm}$. Find its area.

Two diagonals of a rhombus measure $x+2$ and $x-2$. If the area of the rhombus is $16$ $cm^2$, find the value of $x$.

A rhombus has an area of $96$ $cm^2$ and one of its diagonals is $16$ cm. Find the perimeter of the rhombus.

A rhombus shaped plot has a side of $25$ m and one diagonal of $30$ m. What is the cost of leveling the plot at Rs $15$ per square meter?

Find the circumference of a circle whose radius is $3.5\text{ m}$.

If the ratio of the radii of two circles is $1:3$, what is the ratio of their circumferences?

The diameter of a wheel is $70\text{ cm}$. How far does it move in one complete revolution?

Which of these formulas correctly represents the area of a circle with radius $r$?

A circular garden is surrounded by a path of uniform width $3.5$ m. If the diameter of the inner circular garden is $14$ m, find the area of the path. (Take $\pi = \frac{22}{7}$)

Find the area of the largest circle that can be cut out from a square of side $14\text{ cm}$.

If the radius of a circle is increased by $10\%$, by what percentage will its area increase?

The ratio of the radii of two circles is $3:4$. What is the ratio of their areas?

The minute hand of a clock is $14\text{ cm}$ long. How much area does it sweep in $15\text{ minutes}$? (Use $\pi = \frac{22}{7}$)

If the area of a circle is numerically equal to three times its circumference, find the diameter of the circle.

Find the area of the path of width $2$ m around a rectangular pool of length $12$ m and breadth $8$ m.

A race track is in the form of a ring whose inner circumference is $352$ m and outer circumference is $396$ m. Find the width of the track. (Take $\pi = \frac{22}{7}$)

A circular garden of diameter $28$ m has a path of $7$ m width inside it. Find the area of the path. (Take $\pi = \frac{22}{7}$)

A picture $10$ cm by $8$ cm is framed with a $2$ cm wide border. Find the area of the border.

A ring has an inner radius of $x$ cm and an outer radius of $x+2$ cm. If the area of the ring is $44\pi$ cm$^2$, find $x$.

The area of a circle is $616$ cm$^2$. A ring is formed by drawing another circle of radius $21$ cm concentric with it. Find the area of the ring. (Take $\pi = \frac{22}{7}$)

A rectangular lawn $70$ m by $50$ m has two roads each $5$ m wide running through its middle. Find the area of the remaining lawn.

Find the area of a ring whose inner and outer radii are the roots of the equation $x^2 - 12x + 35 = 0$. (Use $\pi = \frac{22}{7}$)

A painting is made on a canvas of length $15\text{ cm}$ and breadth $10\text{ cm}$ such that there is a margin of $1.5\text{ cm}$ along each of its sides. Find the total area of the margin.

From a circular cardboard of radius $14\text{ cm}$, two circles of radius $3.5\text{ cm}$ and a rectangle of $3\text{ cm} \times 1\text{ cm}$ are removed. Find the area of the remaining cardboard. (Use $\pi = \frac{22}{7}$)