Measuring Space: Perimeter and Area

How many meters of lace are required to put around a rectangular table cloth of $2\text{ m}$ long and $1.5\text{ m}$ wide?

Find the length of the side of an equilateral triangle if its perimeter is $45\text{ cm}$.

What is the perimeter of an isosceles right-angled triangle with equal sides of $5\text{ cm}$ and hypotenuse $5\sqrt{2}\text{ cm}$?

The perimeter of a square is $P$. If each side is increased by $2\text{ units}$, the new perimeter is:

The area of a right-angled triangle is $30\text{ cm}^2$ and the length of its hypotenuse is $13\text{ cm}$. Find the perimeter of the triangle.

Find the perimeter of a triangle whose sides are $11\text{ cm}, 60\text{ cm}$ and $61\text{ cm}$.

If the side of a square is tripled, how many times the original perimeter will the new perimeter be?

What is the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15$ cm and $18$ cm?

A rope of length $66$ m is used to form a circle. How many times can a smaller rope of length $1.1$ m fit along the circumference?

Find the perimeter of a rectangle whose diagonal is $17$ cm and length is $15$ cm.

If the diameter of a circle is $42$ cm, what is its circumference? (Use $\pi \approx \frac{22}{7}$)

If $C$ is the circumference and $r$ is the radius, then $\frac{C}{2\pi}$ is:

A circle has a radius of $14$ units. Its circumference is:

If the circumference of a circle is $C$, then $C/2$ is equal to:

The sum of the radii of two circles is $15$ cm and the difference of their circumferences is $44$ cm. What is the radius of the smaller circle? (Use $\pi = \frac{22}{7}$)

If the circumference of a circle is $C$, then its radius $r$ is equal to:

The distance covered by a circular wheel of diameter $d$ in one complete revolution is:

If the circumference of a circle is numerically equal to the perimeter of an equilateral triangle of side $s$, find the radius of the circle in terms of $s$.

If $d_1$ and $d_2$ are the diameters of two circles with circumferences $C_1$ and $C_2$, and $C_1 > C_2$, then which relationship is strictly true regarding the $C/D$ ratio?

If the circumference of a circle is decreased by $50\%$, by what percentage does the diameter decrease?

Is the number $0$ a value for $\pi$?

If the radius of a circle is $r$, the ratio of the area to the circumference is $1:1$ when $r$ is:

The number $\pi^2$ is:

What is the result of $\pi / \pi$ (where $\pi \neq 0$)?

If $x = \pi - 22/7$, then $x$ is:

Which of the following is an irrational number between $3$ and $4$ used in geometry?

If the numerical value of the circumference of a circle is $18\pi$, what is the area of the circle?

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is:

If the area of a sector of a circle of radius $6$ cm is $9\pi$ cm$^2$, what is the length of the arc of the sector?

Given that $\pi$ is irrational, which of the following results for the area of a circle with radius $r = 7$ is the most mathematically accurate?

The perimeter of a semi-circle of radius $r$ is:

Find the arc length of a semicircle with diameter $21$ cm. (Use $\pi = \frac{22}{7}$)

The length of an arc of a circle of radius $14$ cm is $11$ cm. Find the angle subtended by the arc at the center. (Use $\pi = \frac{22}{7}$)

If the length of an arc is $\frac{\pi r}{3}$, what is the central angle?

What is the ratio of the length of an arc subtending an angle of $60^\circ$ at the center to the total circumference of the circle?

Find the perimeter of a semicircle with a radius of $14$ cm. (Use $\pi = \frac{22}{7}$)

The hour hand of a clock is $6$ cm long. Find the distance moved by its tip in $4$ hours. (Leave answer in terms of $\pi$)

If the angle of a sector is $d$ degrees and the radius is $r$, what is the length of the arc?

The perimeter of a sector of a circle is $18\text{ cm}$ and its radius is $3\text{ cm}$. Find the area of the sector.

If the length of an arc of a circle is $1/6$th of the circumference, find the angle of the sector in radians.

In the staircase paradox, a path goes from $(0,0)$ to $(1,1)$ using $N$ steps (each step going right then up). As $N$ increases to infinity, the length of the staircase path is always:

The perimeter of a regular decagon (10 sides) with side $2.5\text{ cm}$ is:

A rectangle has a length of $10\text{ cm}$ and a perimeter of $30\text{ cm}$. Its width is:

Which of these shapes with the same perimeter has the largest area?

If the side of a square is $a$, and it is doubled, the ratio of the new perimeter to the old perimeter is:

The cost of fencing a circular field at the rate of $Rs. 24$ per meter is $Rs. 5280$. What is the radius of the field?

The perimeter of a triangular field is $450 \text{ m}$ and its sides are in the ratio $13:12:5$. Find its area.

Is it possible for a triangle to have sides $7$ cm, $8$ cm, and $16$ cm?

The area of a triangle with sides $a, b, c$ is $K$. If the sides are increased to $ka, kb, kc$, what is the area of the new triangle?

A wire is bent into the shape of a square of area $81$ cm$^2$. If the same wire is bent into a semi-circle, what is the radius of the semi-circle? (Take $\pi = 22/7$)

A rectangle has a width of $7$ units and a length of $9$ units. If the length is increased by $1$ unit, what is the new area?

Find the area of a rectangle whose diagonal is $5$ cm and length is $4$ cm.

A rectangle has an area of $100$ cm$^2$. If its width is $4$ cm, find its length.

If the perimeter of a rectangle is $30$ cm and the length is $10$ cm, what is its area?

A rectangular park $60$ m $\times$ $40$ m has two crossroads, each of width $5$ m, running in the middle of it, one parallel to the length and the other parallel to the width. Find the area of the crossroads.

Find the area of the L-shaped figure shown, which is composed of two rectangles.

If the diagonal of a rectangle is $13$ cm and its width is $5$ cm, find its area.

The cost of fencing a rectangular field at Rs $30$ per meter is Rs $2400$. If the length of the field is $24\text{ m}$, find the area of the field.

A rectangular carpet has an area of $120\text{ m}^2$ and a perimeter of $46\text{ m}$. Find the length of its diagonal.

A wire is in the shape of a square of side $10\text{ cm}$. If the wire is rebent into a rectangle of length $12\text{ cm}$, find its breadth. Which figure encloses more area and by how much?

If the base of a parallelogram is $b$ and altitude is $h$, which formula represents its area?

What is the area of a rhombus if its diagonals are $10\text{ cm}$ and $12\text{ cm}$? (Note: A rhombus is a special parallelogram)

A parallelogram has a base of $7.5\text{ cm}$ and a height of $4\text{ cm}$. Find its area.

In a parallelogram $PQRS$, the altitude $PM$ to the base $SR$ is $5\text{ cm}$ and $SR = 8\text{ cm}$. What is the area?

In a parallelogram $ABCD$, $AB = 15\text{ cm}$ and the area is $120\text{ cm}^2$. If a point $P$ lies on $CD$, what is the area of triangle $ABP$?

A field is in the shape of a parallelogram with a base of $80\text{ m}$ and height of $60\text{ m}$. If the cost of leveling the field is Rs $2$ per square metre, find the total cost.

The area of a parallelogram is $250\text{ cm}^2$. If the ratio of base to height is $5:2$, find the measure of the base.

A park in the shape of a parallelogram $ABCD$ has adjacent sides $AB = 40$ m and $BC = 28$ m. The distance between the longer sides $AB$ and $CD$ is $14$ m. A walking track is being constructed such that it connects the midpoints of sides $AD$ and $BC$, effectively dividing the parallelogram into two smaller congruent parallelograms. Calculate the distance between the shorter sides $AD$ and $BC$ and the area of the upper smaller parallelogram $ABNM$.

A rhombus is a special type of parallelogram. If the diagonals of a rhombus are $16\text{ cm}$ and $12\text{ cm}$, what is the altitude of the rhombus if its side length is $10\text{ cm}$?

A parallelogram has sides $15\text{ cm}$ and $10\text{ cm}$. If one of its diagonals is $20\text{ cm}$, find the area of the parallelogram (Use Heron's formula for the triangle).

What is the area of a triangle with sides 8 cm, 15 cm and 17 cm?

The sides of a triangle are in the ratio 3:4:5 and its perimeter is 36 cm. Find its area.

In a right triangle, if the legs are 6 cm and 8 cm, find the length of the altitude drawn to the hypotenuse.

If the base of a triangle is doubled and its height is halved, what happens to the area?

If the area of an equilateral triangle is $16\sqrt{3}\text{ cm}^2$, find its perimeter.

The height of an equilateral triangle is $6\text{ cm}$. Find its area.

Find the area of an isosceles triangle whose base is $b$ and each equal side is $a$.

The perimeter of a triangular forest is $600$ m. If the sides are in the ratio $5:12:13$, find the area of the forest and check if it is a right-angled triangle.

Two sides of a triangular field are $85$ m and $154$ m and its perimeter is $324$ m. Find the area of the field and the length of the perpendicular from the opposite vertex to the side of $154$ m.

Find the area of a shaded region in a triangle where the outer sides are $20$ cm, $21$ cm, and $29$ cm, and an inner similar triangle is removed whose sides are half of the outer dimensions.

A rectangle has sides in the ratio $1:9$. If its area is $81$ cm$^2$, what is the side of the square with the same area?

A rectangular paper of $20$ cm by $5$ cm is cut and rearranged into a square without any overlap or gaps. What is the side of the square?

A rectangle has a width that is $1/4$ of its length. If the area of the rectangle is $64$ cm$^2$, what is the side of the square with the same area?

A square is drawn such that its side is the geometric mean of the sides of a $4$ by $9$ rectangle. What is the perimeter of this square?

A rectangle has a length of $16\text{ cm}$ and a width of $9\text{ cm}$. A square is constructed such that its area is exactly equal to the area of this rectangle. Find the difference between the perimeter of the rectangle and the perimeter of the square.

Calculate the side of a square whose area is the same as the sum of the areas of two rectangles, one $4 \times 4$ and another $3 \times 12$.

If a square and a rectangle have the same area, and the rectangle's length is four times its width, what is the ratio of the square's side to the rectangle's width?

Geometric squaring of a rectangle with sides $a$ and $b$ can be done using the Mean Proportional theorem. In a semi-circle with diameter $a+b$, a perpendicular is drawn from the junction of $a$ and $b$ to the circumference. If $a=9$ and $b=4$, what is the length of this perpendicular?

A rectangular sheet of metal measures $x$ by $y$. When it is squared (converted to a square of area $A$), the perimeter increases by $10\%$. If the original area was $100\text{ cm}^2$, what is the sum of the side lengths $(x+y)$ of the rectangle?

A farmer has a rectangular field of $32\text{ m} \times 18\text{ m}$. He wants to divide it into smaller square plots of equal area such that no land is wasted and the side of each square is an integer. If he chooses to make the square plots as large as possible, how many such squares will he have?

A circular wire has a radius of $7$ cm. What is the area of the region enclosed by it? (Take $\pi = \frac{22}{7}$)

Find the area of a circle with a radius of $6$ cm. (Take $\pi = 3.14$)

The area of a circle of radius $8$ cm is how many times the area of a circle of radius $2$ cm?

If the circumference of a circle is $22$ cm, find its area. (Take $\pi = \frac{22}{7}$)

A rectangular piece of cardboard measures $25\text{ cm}$ by $20\text{ cm}$. If the largest possible circle is cut out from this cardboard, what is the area of the remaining portion? (Take $\pi = 3.14$)

What is the area of a circle whose diameter is $d$?

Find the area of a circle where the circumference is equal to the perimeter of a square of side $11\text{ cm}$.

If the circumference of a circle is $C$, then its area is given by: