Area of a Triangle

Q. Area of triangle with vertices (x_1, y₁), (x_2, y₂) & (x_3, y₃) is given by _______.

1. ½[ x₁(y₂+y₃) - x₂(y₃+y₁) - x₃(y₁+y₂)]
2. ½[ x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]
3. ½[ x₁(y₂-y₃) - x₂(y₃-y₁) + x₃(y₁-y₂)]
4. ½[ x₁(y₂-y₃) + x₂(y₃-y₁) - x₃(y₁-y₂)]

Q.

If the perimeter of the equilateral triangle is $180$ $cm$, what will be its area?

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.

Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.

Q.

A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides (Fig). Find the radius of the inscribed circle and the area of the shaded part.

Q. The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. The area of the triangle is

1. $70c{m}^2$
2. $140c{m}^2$
3. $210c{m}^2$
4. $420c{m}^2$

Q. The height of atriangle is 6cms more than the base.area of the triangle is 108cm2 . find the length of the base

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.

The base of an isosceles triangle is $8cm$ long and each of its equal sides measures $6cm$. The area of the triangle is

1. $8\sqrt{5}c{m}^2$

2. $16\sqrt{5}c{m}^2$

3. $16\sqrt{3}c{m}^2$

4. $8\sqrt{3}c{m}^2$

Q.

Three horses are tethered with 7 meter long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. The area of the plot which can be grazed by the horses is

1. 80 m²

2. 100 m²

3. 30 m²

4. 77 m²

Q.

The area of a right triangle is 600 $c{m}^2$. If the base of the triangle exceed the altitude by 10 cm, find the dimensions of the triangle.

Q.

Find the condition that the point P(x, y) may lie on the line joining (3, 4) and (-5, -6).

1. $5x+4y-1=0$

2. $5x-4y-1=0$

3. $5x+4y+1=0$

4. $5x-4y+1=0$

Q.

Each of the equal sides of an isosceles triangle is $13cm$ and its base is $24cm$. The area of the triangle is

1. $156c{m}^2$

2. $60c{m}^2$

3. $78c{m}^2$

4. $120c{m}^2$

Q.

Calculate the area of the triangle whose sides are 12 cm, 17 cm and 25 cm.

1. $190c{m}^2$

2. $180c{m}^2$

3. $10c{m}^2$

4. $90c{m}^2$

Q.

The base of a right-angled triangle measures 48 cm and its hypotenuse measures 50 cm. Find the area of the triangle.

Q.

The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle.

Q.

The hypotenuse of a right-angled triangle is 65 cm and its base is 60 cm. Find the length of perpendicular and the area of the triangle.

Q. The area of right-angled triangle is 96m³. If its base is three times its altitude, find the base.

Q.

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [ Use $\sqrt{3}1.732and\pi =3.14$]

Q.

Each of the equal sides of an isosceles triangles measures 2 cm more than its height, and the base of the triangle measures 12 cm. Find the area of the triangle.

Q.

The area of a right-angled triangle is 165 sq metres. Determine its base and altitude if the latter exceeds the former by 7 metres.

Q.

If the height and base of the right triangle is 12 cm and 9 cm resp., the area of the triangle is __ $c{m}^2$.

Q.

The sides of a triangle are in the ratio $5:12:13$, and its perimeter is $150m$. Find the area of the triangle.

Q.

The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the areah of the triangle is 24 $c{m}^2$, find the perimeter of the triangle.

Q.

The difference between the sides at right angles in a right-angled triangle is 7 cm, The area of the triangle is 60 $c{m}^2$. Find its perimeter.

Q.

The lengths of the three sides of a triangle are $20cm$, $16cm$ and $12cm$. The area of the triangle is

1. $96c{m}^2$

2. $144c{m}^2$

3. $120c{m}^2$

4. $160c{m}^2$

Q.

Calculate the area of a quadrilateral $ABCD$ when the length of the diagonal $AC=10cm$ and the lengths of perpendiculars from $B$and $D$ on $AC$ be $5cm$ and $6cm$ respectively.

Q.

The base and height of a triangle are in the ration $3:4$ and its area is $216c{m}^2$. The height of the triangle is

$\left(a\right)16cm\left(b\right)24cm\left(c\right)21cm\left(d\right)28cm$

Q. The area of sector is one-twelfth that of the complete circle. Find the angle of the sector .

Q.

The side of an equilateral triangle is equal to the radius of a circle whose area is 154 $c{m}^2$. The area of the triangle is

(a) 49 $c{m}^2$ (b) $\frac{49\sqrt{3}}{4}c{m}^2$ (c) $\frac{7\sqrt{3}}{4}c{m}^2$ (d) 77 $c{m}^2$