Heron's Formula

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

1. 48 cm
2. 24 cm
3. 12 cm
4. 36 cm

Q.

Assertion: The sides of a triangle are 3cm, 4cm and 5cm. Its area is $6c{m}^2$

Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area

$=\sqrt{(s-a)(s-b)(s-c)}$

Which of the following is correct?

1. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3. The assertion is correct but Reason is incorrect.

4. The assertion is incorrect but Reason is correct.

Q.

The sides of a triangle are 16 cm, 12 cm and 20 cm. Find:

(i) Area of the triangle

(ii) Height of the triangle, corresponding to the largest side

(iii) Height of the triangle, corresponding to the smallest side.

Q.

The lengths of the sides of a triangle are in the ratio 4 : 5 : 3 and its perimeter is 96 cm. Find its area.

Q.

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

1. 8√2

2. 7√2

3. 4√2

4. 16√2

Q.

Tho adjacent sides of a parallelogram are 21 cm and 28 cm. If its one diagonal is 35 cm; find the area of the parallelogram.

Q.

The area of a triangle with sides 21cm, 20 cm and 13 cm is___ sq cm.

1. 70

2. 120

3. 63

4. 126

Q.

Area of a right-angled triangle is $30c{m}^2$. If its smallest side is $5cm$, then its hypotenuse is

1. $14cm$

2. $13cm$

3. $12cm$

4. $11cm$

Q.

Assertion: The sides of a $\Delta ABC$ are in the ratio 2:3:4 and its perimeter is 36cm. Then, $ar\left(\Delta ABC\right)=12\sqrt{15}c{m}^2$

Reason: If where a, b, c are the sides of a triangle, $\frac{s=(a+b+c)}{2}$, then its area $=\sqrt{(s-a)(s-b)(s-c)}$

Which of the following is correct?

1. A and R are true and R is the correct explanation of A.

2. A and R are true and R is not the correct explanation of A.

3. A is false and R is true.

4. A is true and R is false.

Q. If the sides of a right-angled triangle are in ratio 3 : 4 : 5, and its perimeter is 48 cm, then its area (in $c{m}^2$) is ___.

1. 30
2. 45
3. 96
4. 135

Q.

Question 10 (i)

In the following figure, find the area of the shaded portion:

Q. The perimeter of a triangular plot is 750 m. If the sides are in the ratio 5 : 12 : 13, then find the area of the plot.

1. 18, 750 sq. m
2. 20, 250 sq.m
3. 21, 050 sq.m
4. 19, 550 sq. m

Q.

The perimeter of an equilateral triangle is 60m. The area is

1. $10\sqrt{3}{m}^2$

2. $15\sqrt{3}{m}^2$

3. $20\sqrt{3}{m}^2$

4. $100\sqrt{3}{m}^2$

Q. In the below figure, $△ABC$ is equilateral with point O as its circumcentre. Here, area of $△BOC$ is equal to area of ____.

1. $\frac{1}{3}△ABC$
2. $△ABC$
3. $\frac{1}{2}△ABC$
4. $\frac{1}{4}△ABC$

Q. The semi-perimeter 's' of a triangle having sides $\text{12, 9 and 15}$ is ___.

Q. The perimeter of a triangular field is $135cm$ and its sides are in the ratio $25:17:12$. Find its area.

Q.

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

1. 500 √15

2. 100 √15

3. 800 √15

4. 200 √15

Q.

A person walks at the rate of $5km/h$. How long will he take to go a round a square park $8$ times whose area is $900m^2$.

Q.

Two equilateral triangle has their sides in ration 3:5 what will be the ratio of their area and perimeter respectively.

1. 3:5 and 9:16

2. 9:25 and 3:5

3. 9:25 and 2:5

4. 9:25 and 3:4

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

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

Q.

A dance floor has to be built as a triangular glass platform with the dimensions $\text{7 m, 8 m and 9 m}$. The total surface area of the glass required to build such a platform is equal to ________ $m^2$.

1. 12√5

2. 6

3. 5√5

4. 5

Q. In an express train the number of passengers travelling in AC sleeper class, first class, and sleeper class are in the ratio 1 : 2 : 3 and the fares of each classes are in the ratio 5 : 4 : 2. If the total income from this train is Rs. 54000, then what is the income from AC sleeper class ?

1. Rs. 11210 (approx)
2. Rs. 13210 (approx)
3. Rs. 14210 (approx)
4. Rs. 16210 (approx)

Q. Find the area of triangle two sides of which are $16cm$ and $22cm$ and perimeter is $64cm$.

Q. An equilateral triangle, a square and a circle have equal perimeters. If $T$ denotes the area of the triangle, $S$ is the area of the square and $C$ the area of the circle, then:

1. $S<T<C$
2. $T<C<S$
3. $T<S<C$
4. $C<S<T$

Q.

Students of a school staged a rally for cleanliness campaign in two groups. Group A walked through the lanes AB, BC and CA, while Group B walked through AC, CD and DA. They cleaned the area enclosed within their lanes. If $\text{AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and}\angle \text{B = 90°}$, which group cleaned more area. Also, find the total area cleaned by the students?

1. Group A and 306 m²

2. Group A and 180 m²

3. Group B and 126 m²

4. Group B and 54 m²

Q.

A triangle with sides 12, 16 and 20 units is given.

Statement 1: To find the area of this triangle, the formula "$Area=\frac{1}{2}\times base\times height$" is the ideal one to be used.

Statement 2: To find the area, the formula "$Area=\sqrt{s(s-a)(s-b)(s-c)}$" is the ideal one to be used.

​Enter “1” if you feel Statement 1 is correct, or “2” if Statement 2 is correct.
___

Q.

A triangle with area $25$ sq. units is translated from one place to another. What is the area of the triangle at its final position?

1. $25$ sq. units

2. $10$ sq. units

3. $20$ sq. units

4. $50$ sq. units

Q. Expand ${(\pi -\frac{22}{7})}^2$ using appropriate identity

Q. A dance floor has to be built as a triangular glass platform with the dimensions 7 m, 8 m and 9 m. The total surface area of the glass required to build such a platform is equal to ________ $m^2$.

1. 5√5

2. 12√5

3. 5

4. 6

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

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

4. 100$\sqrt{\left(15\right)}$