Area of Special Triangles

Q.

$\frac{1}{2}\times \text{base}\times \text{height}$ is the formula of area for which type of triangles?

1. Only right angled triangles

2. Only isosceles triangle

3. All type of triangles

4. None of these

Q.

Area of the triangle whose sides are 13cm, 9cm and 6cm is

1. $23.6m^2$

2. $26.3m^2$

3. $36.34m^2$

4. $23.66m^2$

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

1. 8 cm
2. 36 cm
3. 4 cm
4. 6 cm

Q. An isosceles triangle has a perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Q. A park, in the shape of a quadrilateral ABCD, has $\angle C={90}^{\circ },\text{AB}=9m,\text{BC}=12m,\text{CD}=5m\text{and AD}=8m$. How much area does it occupy?
(3 Marks)

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

Q.

The base of a triangular field is 2.4 times its height. If the cost of levelling the field at the rate of ₹20 per square meter is ₹9600, then the height of the field is ___ m.

1. 48

2. 50

3. 20

4. 30

Q. If the area of an equilateral triangle is $36\sqrt{3}{\text{cm}}^2$. Find the length of its side and perimeter.

Q. If the hypotenuse and one side of a right angle triangle are 13 cm and 12 cm respectively, then its area is 30 $c{m}^2$.

1. False
2. True

Q.

What is the area of an equilateral triangle whose side is $\text{8 cm}$?

1. 16√3cm²

2. 16cm²

3. 16√5 cm²

4. 6√3cm²

Q.

Find the area of the equilateral triangle given below:

Given: AD=10 cm.

1. $100c{m}^2$

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

3. $25\sqrt{3}c{m}^2$

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

Q. If the perimeter of an equilateral triangle is 60 cm, then its area is 1732 $c{m}^2$.

1. False
2. True

Q.

If the area of an equilateral triangle is $25\sqrt{3}c{m}^2$, then its perimeter = ____ cm.

1. 30

2. 45

3. 10

4. 60

Q. Find the area of the right-angled triangle with hypotenuse 40cm and one of the other two sides 24cm

Q. Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm?

Q.

Statement 1: In an equilateral triangle, the heights onto all the sides are equal.
Statement 2: The base lengths are also equal in an equilateral triangle.

1. Statement 1 is correct but statement 2 is incorrect

2. Statement 1 is incorrect but statement 2 is correct

3. Both the statements are correct

4. Both the statements are incorrect

Q.

If an isosceles right - angled triangle has area $200c{m}^2$, then the measure of its hypotenuse is ___ cm.

1. $10\sqrt{2}$

2. 10

3. 20

4. $20\sqrt{2}$

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

1. $8$ cm
2. $4$ cm
3. $36$ cm
4. $6$ cm