Properties of Triangles

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.

How does the following organism reproduce by asexual methods?

Agaricus

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

(a) 70 cm²

(b) 140 cm²

(c) 210 cm²

(d) 420 cm²

Q. The area of incircle of an equilateral triangle is 154 cm² . The perimeter of the triangle is

(a) 71.5 cm

(b) 71.7 cm

(c) 72.3 cm

(d) 72.7 cm

Q.

A lateral faces of a square pyramid are equilateral triangles of side 30 centimetres. What is its surface area?

Q. The area of an equilateral triangle is $4\sqrt{3}{\mathrm{cm}}^2$. Its perimeter is
(a) 9 cm
(b) 12 cm
(c) $4\sqrt{3}$ cm
(d) $\frac{3\sqrt{3}}{4}$ cm

Q. The difference between the sides of right angles in a right angles triangle is 14 cm .The area of the triangle is 120 cm sq . Calculate the perimeter of the triangle

Q. Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm². Also, find its perimeter. Take $\sqrt{2}$ = 1.414.

Q. The area of an equilateral triangle is $4\sqrt{3}{\mathrm{cm}}^2$. Its perimeter is
(a) 9 cm
(b) 12 cm
(c) $12\sqrt{3}$ cm
(d) $6\sqrt{3}$ cm

Q. Each side of an equilateral triangle measures 8 cm. Find (i) the area of the triangle, correct to 2 decimal places, and (ii) the height of the triangle, correct to 2 places of decimal. Take $\sqrt{3}=1.732.$

Q. How to find a area of a triangle whose on angle is 60: and two sides are 42 cm and 42cm (triangle is in a sector)

Q. Each side of an equilateral triangle is 8 cm. Its area is
(a) 24 cm²
(b) $24\sqrt{3}{\mathrm{cm}}^2$
(c) $16\sqrt{3}{\mathrm{cm}}^2$
(d) $8\sqrt{3}{\mathrm{cm}}^2$

Q. Find the area of the triangle whose sides are 18 cm, 24 cm and 30 cm. Also, find the height corresponding to the smallest side.

Q. Find the area of the equilateral triangle whose each side is (a)12 cm (b)5cm

Q. Each side of an equilateral triangle measures 8 cm. Its area is
(a) $2\sqrt{3}{\mathrm{cm}}^2$
(b) $16\sqrt{3}{\mathrm{cm}}^2$
(c) 32 cm²
(d) 64 cm²

Q. What is the value of perimeter of a triangle, if the inradius is 5 cm and area is 10 sq. cm?

1. 4 cm
2. 2 cm
3. 6 cm
4. 5 cm

Q.

In the given fig. a circle is inscribed in a quadrilateral ABCD in which $\angle$B = ${90}^0$. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

Q. Two sides of a triangular field are 85 m and 154 m in length, and its perimeter is 324 m. Find (i) the area of the field, and (ii) the length of the perpendicular from the opposite vertex on the side measuring 154 m.

Q. A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12 m. If the length of the rope is 7 m, find the area of the field which the horse cannot graze. Write the answer correct to 2 places of decimal.

Q.

In a circle, O is the centre and $\angle$COD is right angle. AC = BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

1. BD = 41.42 cm

2. OD = 141.42 cm

3. PD = 100 cm

4. AC + CP = 141.42 cm

Q. Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. Find the height corresponding to the longest side.

Q. If the area of an equilateral triangle is , find its height.

Q. The side of an equilateral triangle is the same as the radius of a circle whose area is 154 cm². The area of the triangle is
(a) $\frac{7\sqrt{3}}{4}{\mathrm{cm}}^2$
(b) $\frac{49\sqrt{3}}{4}{\mathrm{cm}}^2$
(c) 35 cm²
(d) 49 cm²

Q. The height of an equilateral triangle is 6 cm. Find its area. [Take $\sqrt{3}$ = 1.73]

Q. The side of an equilateral ?ABC is 7cm. Find the side of another equilateral ?PQR whose area is 3times the area of ?ABC.

Q. The side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm². The area of the triangle is
(a) 49 cm²
(b) $\frac{49\sqrt{3}}{4}{\mathrm{cm}}^2$
(c) $\frac{7\sqrt{3}}{4}{\mathrm{cm}}^2$
(d) 77 cm²

Q. Choose the correct answer of the following question:

The height of an equilateral triangle is $3\sqrt{3}$ cm. Its area is

(a) $6\sqrt{3}$ cm² (b) 27 cm² (c) $9\sqrt{3}$ cm² (d) $27\sqrt{3}$ cm²

Q. If each side of an equilateral triangle is 8 cm long, then its area is cm².

Q. Find the area of an equilateral triangle having each side of length 10 cm.

Q.

A lateral faces of a square pyramid are equilateral triangles of side 30 centimetres. What is its surface area?