Area of a Triangle

Q.

Find the area of a triangle whose sides area 3 cm, 4 cm and 5cm respectively.

Q.

The perimeter of an isosceles triangle is $32\mathrm{cm}$.

The ratio of the equal side to its base is $3:2$.

Find the area of the triangle.

Q.

The altitude of an isosceles triangle is $8cm$ and the perimeter is $32cm.$ Calculate the area of the triangle.

1. $48c{m}^2$

2. $54c{m}^2$

3. $60c{m}^2$

4. None of these

Q.

If the sides of a triangle are a, b and c. Then, what is the semi perimeter of the triangle?

1. (a+b+c)/2

2. (a+b+c)/4

3. $\frac{a+b+c}{3}$

4. (a+b+c)

Q.

$\text{The base of a right triangle is 48 cm and its hypotenuse is 50 cm long.The area of the triangle is}\left(a\right)168c{m}^2\left(b\right)252c{m}^2\left(c\right)336c{m}^2\left(d\right)504c{m}^2$

Q.

The base of a triangular field is three times its altitude. If the cost of sowing seeds in the field at 58/- per hectare is 783/-, find base and altitude.

Q.

Let $a$ and $b$ be positive real numbers. Suppose $\overrightarrow{PQ}=a\hat{i}+b\hat{j}\text{and}\overrightarrow{PS}=a\hat{i}-b\hat{j}$​ are adjacent sides of a parallelogram $PQRS$. Let $u$ and$v$ be the projection vectors of $\overrightarrow{w}=\hat{i}+{\hat{j}}^{}$ along $\overrightarrow{PQ}\text{and}\overrightarrow{PS}$ respectively. If $\mid u\mid +\mid v\mid =\mid w\mid$ and if the area of the parallelogram $PQRS$ is $8$, then which of the following statements is/are TRUE?

1. $a+b=4$

2. $a–b=2$

3. The length of the diagonal $\overrightarrow{PR}$ of the parallelogram is $4$

4. $\overrightarrow{w}$is an angle bisector of the vectors $\overrightarrow{PQ}\text{and}\overrightarrow{PS}$

Q.

The base and hypotenuse of a right triangle are respectively 5cm and 13cm long. Its area is

1. $30c{m}^2$

2. $40c{m}^2$

3. $25c{m}^2$

4. $28c{m}^2$

Q.

If all the three altitudes of a triangle are equal, the triangle is equilateral.

Prove it.

Q.

Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.

Q.

ABCD is a trapezium in which AB || DC. If $ar\left(△ABD\right)=24c{m}^2$ and AB = 8 cm, then height of$△ABC$ is

1. 3 cm

2. 4 cm

3. 6 cm

4. 8 cm

Q.

$\text{Each of the two equal sides of an isosceles right triangle is 10 cm long. Its area is}\left(a\right)5\sqrt{10}c{m}^2\left(b\right)50c{m}^2\left(c\right)10\sqrt{3}c{m}^2\left(d\right)75c{m}^2$

Q.

$Ina\Delta ABC,\text{it is given that base = 12 cm and height = 5 cm. Its area is}\left(a\right)60c{m}^2\left(b\right)30c{m}^2\left(c\right)15\sqrt{3}c{m}^2\left(d\right)45c{m}^2$

Q.

IN the figure, ABCD is a trapezium in Which AB = 7 cm, AD = BC = 5 cm, DC = x cm, and distance between AB and DC is 4 cm.
Find the value fo x and area of trapezium ABCD.

Q.

The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is

1. $\frac{15\sqrt{7}}{4}cm$
   

2. $\frac{15\sqrt{7}}{2}cm$
   

3. $30\sqrt{7}cm$
   

4. 30 cm

Q.

In the given figure, ABCD is a trapezium such that $AL\perp DC$ and $BM\perp DC$.If AB=7 cm, BC=AD=5 cm and AL=BM=4 cm then ar(trap.ABCD)=?

(a) $24c{m}^2$

(b) $40c{m}^2$

(c) $55c{m}^2$

(d) $27.5c{m}^2$

Q.

In the figure, the ratio of AD to DC is 3 to 2. If the area of $\Delta$ ABC is $40c{m}^2$, what is the area of $\Delta BDC$?

1. $24c{m}^2$

2. $36c{m}^2$

3. $30c{m}^2$

4. $16c{m}^2$

Q.

A rectangle with one side 4 cm is inscribed in a circle of radius 2.5cm . Find the area of the rectangle

Q. Find the area of the triangular field of sides 55 𝑚, 60 𝑚, and 65 𝑚. Find the cost of laying the grass in the triangular field at the rate of ₹8 per $m^2$.

Q.

In the figure, $\angle AOB={90}^{\circ },AC=BC,OA=12$ cm and $OC=6.5cm$. Find the area of $△AOB$

Q.

In the figure, PQRS is a square and T and U are respectively, the midpoints of PS and QR. Find the area $△OTS$ if PQ = 8 cm.

Q.

In the adjoining figure, the point D divides the side BC of $△ABC$ in the ratio m:n.Prove that $\left(△ABD\right):ar\left(△ADC\right)=m:n$.

Q.

The sides of a triangular field are $20m$, $37m$ and $51m$. Find the number of flower beds that can be prepared if each bed measures $(2\times 3)m^2$ .

Q.

In triangle PQR, PR = 8 cm, QR = 8 cm and PL = 5 cm. Find the area of triangle PQR.

1. $5c{m}^2$

2. $15c{m}^2$

3. $18c{m}^2$

4. $20c{m}^2$

Q. In a parallelogram ABCD, the diagonal AC measures 34 m and the perpendicular distance of AC from either of the vertices B or D is 12 m. Find the area of the parallelogram.

1. 204 sq. m
2. 408 sq. m
3. 816 sq. m
4. 806 sq. m

Q.

Through $A,B$ and $C$ lines $RQ,PR$ and $QP$ have been drawn, respectively parallel to sides $BC,CA$ and $AB$ of a $\Delta ABC$ as shown in figure. Show that $BC=\frac{1}{2}QR$.

Q.

If the sides of a triangle is 20cm, 24cm and 25cm.Find the semi perimeter of the triangle. [1 MARK]

Q.

The base of an isosceles triangle measures 80 cm and its area is 360 $c{m}^2.$ Find the perimeter of the triangle.

Q. Question 7
ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects CD at F.
If ar (DFB) = 3 $c{m}^2$, find the area of the parallelogram ABCD.

Q.

Let ABC be a triangle of area 24 sq. units and PQR be the triangle formed by the midpoints of sides of $△ABC.$ Then the area of $△PQR$ is