Use of Algebraic Expressions in Formula of Area of Figures

Q. The length and breadth of a rectangular plot are $l$ and $b$ units respectively. Two rectangular paths each of width $w$ units run inside the plot one parallel to the length and the other parallel to the breadth. What is the total area (in sq. units) of the paths?

1. $lb-(l-w)(b-w)$
2. $(l+b-w)w$
3. $lb-(l-2w)(b-2)$
4. $(l+w)(b+w)-lb$

Q. Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.

Q.

The length of a rectangle is twice its breadth. If its area is 72 sq m, then the breadth of the rectangle is ____.

1. 24 m

2. 12 m

3. 6 m

4. 72 m

Q.

Question 80

The rate of planting the grass is Rs. x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.

Q.

Amisha has a square plot of side ${}^{\prime }{m}^{\prime }$ and another triangular plot with base and height each equal to ${}^{\prime }{m}^{\prime }.$ What is the total area of both plots?

Q. The sides of a right angled triangle are 2a cm, (2a+2) cm and (4a -2) cm long. What is the length of the shortest side of the triangle if its perimeter is 24 cm?

1. 8 cm
2. 6 cm
3. 10 cm
4. 3 cm

Q.

Twenty years from now, Arjun will become three times as old as he is now. His present age is ___ years.

Q. Find the area of a rectangle whose length is $5xy$ cm and breadth is $8x{y}^2$ cm when $x=2$ and $y=3$.

1. $4320c{m}^2$
2. $4820c{m}^2$
3. $3620c{m}^2$
4. $3520c{m}^2$

Q.

Question 53 (g)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Area of a triangle with base m and height n.

Q. A rectangle is 3p cm long and 2p cm wide. Find the perimeter of the rectangle when p = 12.

1. 102 cm
2. 120 cm
3. 210 cm
4. 10p cm

Q.

The length of a rectangular field is one more than twice of the breadth. What is its area if the breadth is x?

1. 2x-1

2. 2x²-x

3. x²+2x

4. 2x²+x

Q.

Write the given statement in the form of algebraic expression and write whether it is monomial, binomial or trinomial: Area of a triangle with base $m$ and height $n$.

Q.

The sides of a right angled triangle are 2a cm, (2a+2) cm and (4a -2) cm. What is the length of the shortest side of the triangle if its perimeter is 24 cm?

1. 3 cm

2. 8 cm

3. 6 cm

4. 10 cm

Q.

Question 26

Fill in the blanks to make the statement true
${\left(\frac{-1}{4}\right)}^3\times \text{\_\_}={\left(\frac{-1}{4}\right)}^{11}$

Q.

If base and the altitude of a triangle are $(3m+2n)$ and $(3m-4n)$ repectively, then the area of the triangle is _____.

1. $\frac{1}{2}\times (9m^2+6mn-8n^2)$

2. $\frac{1}{2}\times (9m^2-6mn+8n^2)$

3. $\frac{1}{2}\times (9m^2-6mn-8n^2)$

4. $\frac{1}{2}\times (9m^2+6mn+8n^2)$

Q. When the perimeter and area of a square are numerically equal, then the numerical value of its side is:

1. $1$
2. $2$
3. $8$
4. $4$

Q. The length of the rectangle is (4ab + 6) m and breadth of the rectangle is $(6b^2+2ab)$ m. Find the area of the rectangle.

1. $(24a{b}^3+18a^2{b}^2+36b^2+12ab)m^2$.
2. $(24a{b}^3+6a^2{b}^2+6b^2+12ab)m^2$
3. $(24a{b}^3+8a^2{b}^2+36b^2+12ab)m^2$
4. $(8a^2{b}^2+36b^2+ab)m^2$.

Q. The base of triangle is $4cm$ longer than its altitudes. If the area of the triangle is $48sq.cm$ then find its base and altitudes.

Q. Consider a square of side length $1$ unit. What is its area?

Q. Find the area of a triangle whose base and altitudes are $8cm$ and $5cm$.

Q. The length of the rectangle is (4ab + 6) m and breadth of the rectangle is $(6b^2+2ab)$ m. Find the area of the rectangle, if $a=2$ and $b=1.$

1. $392m^2$
2. $362m^2$
3. $372m^2$
4. $396m^2$

Q. Find the area of the square, if its side measures $3x^2$ metre.

1. $9x^4$
2. $6x^4$
3. $3x^4$
4. $9x^3$

Q. In the given figure, each square contains four square grid of equal dimensions. Then calculate the area of the given figure.

1. $16c{m}^2$
2. $20c{m}^2$
3. $28c{m}^2$
4. $24c{m}^2$

Q.

A man X has a land whose area is $3^4$ metre square and a man Y has $4^3$ metre square of land. If the land costs Rs 50 per meter square, who has higher property value? [4 MARKS]

Q.

If the sides of a triangle are $4cm,6cm$ and $6cm,$ then find the height corresponding to the smallest side.

1. 16√2

2. 8√2

3. 4√2

4. 7√2

Q. The length and breadth of a rectangular plot are $l$ and $b$ units respectively. Two rectangular paths each of width $w$ units run inside the plot one parallel to the length and the other parallel to the breadth. What is the total area (in sq. units) of the paths?

1. $(l+w)(b+w)-lb$
2. $(l+b-w)w$
3. $lb-(l-w)(b-w)$
4. $lb-(l-2w)(b-2)$

Q. The number of significant digits in the measurement of the side of a square whose computed area is $1.1025$ square inches to the nearest tenthousandth of a square cm is

1. $2$
2. $3$
3. $4$
4. $5$
5. $1$

Q. Write the following statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial.
Area of a triangle with base $m$ and height $n$

Q. The area of a rectangle is $6x^2-4xy-10y^2$ square unit and its length is $2x+2y$ unit. Find its breadth.

Q. Show that :
${\left\{{\left(x^{a-a^1}\right)}^{\frac{1}{a-1}}\right\}}^{\frac{a}{a+1}}=x$