Heron's Formula

Q. The sides of a triangle are in the ratio 12: 17: 25 and its perimeter is 540 cm. What is its area.

1. 5000 sq. cm
2. 6000 sq. cm
3. 9000 sq. cm
4. 8000 sq. cm

Q. Find the area of the triangle whose sides are 8cm 6cm and 7cm by Herons Formula

Q. Find the area of a parallelogram given in the figure. Also, find the length of the altitude from vertex A on the side DC.

1. $180{\text{cm}}^2,15\text{cm}$
2. $150{\text{cm}}^2,15\text{cm}$
3. $150{\text{cm}}^2,10\text{cm}$
4. $180{\text{cm}}^2,10\text{cm}$

Q.

The sides of a triangle park are in ratio 3:5:7, if its perimeter is 90 m, Find its area.

1. = $135m^2$

2. = $135\sqrt{3}{m}^2$

3. = $132\sqrt{3}{m}^2$

4. = $138\sqrt{3}{m}^2$

Q. The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.

1. $1050\sqrt{7}{m}^2$
2. $1050\sqrt{15}{m}^2$
3. $2100\sqrt{15}{m}^2$
4. $420\sqrt{15}{m}^2$

Q. If an isosceles triangle has perimeter 18 cm and base 8 cm, then its area is ${cm}^2$.

1. $45c{m}^2$
2. $24c{m}^2$
3. $36c{m}^2$
4. $12c{m}^2$

Q. Using Heron's Formula, find the area of an isosceles triangle, ​the measure of one of its equal sides being 'a' units and the ​third side '2b' units.

1. $b\sqrt{a^2-b^2}sq.units$
2. $a\sqrt{a^2+b^2}sq.units$
3. $a\sqrt{a^2-b^2}sq.units$
4. $b\sqrt{a^2+b^2}sq.units$

Q. The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300 m. Find the area of the plot.

1. $1500\sqrt{2}{m}^2$
2. $1500\sqrt{3}{m}^2$
3. $1425\sqrt{2}{m}^2$
4. $1500m^2$

Q. Question 5
The length of each side of an equilateral triangle having an area of $9\sqrt{3}c{m}^2$ is

Q. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2.
Find the area of the triangle.

Q. The sides of a triangle are in the ratio 12: 17: 25 and its perimeter is 540cm. The area is:

1. 1000 sq.cm
2. 5000 sq.cm.
3. 9000 sq.cm.
4. 8000 sq.cm.

Q. Match the below figures with their respective areas in $c{m}^2$.

1. $6+2\sqrt{2}1$
2. 306
3. 114

Q. The sides of a triangular plot are in the ratio $4:5:6$ and its perimeter is $150$ cm. Then the sides are

1. $4cm,5cm,6cm$
2. $40cm,50cm,60cm$
3. $8cm,10cm,12cm$
4. $120cm,150cm,180cm$

Q. The area of a triangle of sides 7 m, 8 m and 9 m is equal to $m^2$.

1. $5\sqrt{5}$
2. $5\sqrt{12}$
3. $12\sqrt{5}$

Q. Herons formula for area of triangle, A; semiperimeter, s and sides a, b, c is given by

Q. In the figure, $\Delta ABC$ has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of $\Delta ABC$ is constructed. Find the height DF of the parallelogram.

1. 1 cm
2. 2 cm
3. 3 cm
4. 4 cm

Q. Question 7
The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.

Q.

The sides of a triangle are in the ratio $1:2:2$ and its perimeter is $500\text{m}$. Then, area of the triangle is:

Q. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. The area of the triangle is sq cm.

1. $32\sqrt{2}c{m}^2$
2. $32c{m}^2$
3. $32\sqrt{4}c{m}^2$

Q. Find the zeroes of the following polynomial:

1. 1
2. 2
3. 3
4. 4

Q.

If the area of an equilateral triangle is $16\sqrt{3}c{m}^2$, then the perimeter of the triangle is

1. 24 cm

2. 12 cm

3. 48 cm

4. 36 cm

Q. The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the height corresponding to the longest side.

Q.

A triangle and a parallelogram have the same base and same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

1. 14 cm

2. 16 cm

3. 10 cm

4. 12 cm

Q. Calculate the area of the triangle whose sides are $18$ cm, $24$ cm and $30$ cm in length. Also find the length of the altitude corresponding to the smallest side.

1. $216{\text{cm}}^2,24$ cm
2. $225{\text{cm}}^2,25$ cm
3. $220{\text{cm}}^2,25$ cm
4. $168{\text{cm}}^2,19$ cm

Q. $△ABC$ is right angled at $A.AB=60cm,AC=80cm$ and $BC=100cm$. D is a point between B and C such that $△ADB$ and $△ADC$ have equal perimeters. What is the length of $BD$?

1. $10cm$
2. $20cm$
3. $60cm$
4. $40cm$

Q.

Fill in the blanks choosing the appropriate option.

According to Herons formula if $\mathrm{s}$ is the $\left(\mathrm{P}\right)$ of a triangle and $a,b,c$ are the three sides of the triangle respectively, then the area of the triangle is $\left(\mathrm{Q}\right)$

1. $\left(\mathrm{P}\right)$ - perimeter,
   $\left(Q\right)=\sqrt{s(s-a)\left(s-b\left)\right(s-c)\right.}$

2. $\left(\mathrm{P}\right)$-semi-perimeter,

   $\left(Q\right)={\left[\frac{1}{s(s-a)(s-b)(s-c)}\right]}^{-\frac{1}{2}}$

3. $\left(\mathrm{P}\right)$ - semi-perimeter,
   $\left(Q\right)=\left[s(s-a){\left(s-b\left)\right(s-c)\right]}^{-1/2}\right.$

4. $\left(\mathrm{P}\right)$ - perimeter,
   $\left(Q\right)=\left[s(s-a){\left(s-b\left)\right(s-c)\right]}^{-1/2}\right.$

Q.

The sides of a triangle are in the ratio $1:2:2$ and its perimeter is $500m$. The area of the triangle in $m^2$ is:

1. 500$\sqrt{\left(15\right)}$

2. 100$\sqrt{\left(15\right)}$

3. 800$\sqrt{\left(15\right)}$

4. 200$\sqrt{\left(15\right)}$

Q.

Find the area of the triangle if the sides of the triangle are in the ratio 12:17:25 and the perimeter of the triangle is 270 m.

1. 2150 $m^2$

2. 2250 $m^2$

3. 2350 $m^2$

4. 2450 $m^2$

Q. The perimeter of a triangle is 50 cm. One side of a triangle is 4cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.

Q. The sides of a triangle are $50cm,78cm$ and $112cm.$ The smallest altitude is