Question 1: Find the area of a triangle with base and height .

Answer:

Area of a triangle

Question 2: The area of a triangle is . Its base is . What is its altitude?

Answer:

Let the height of the triangle

Area of triangle

Question 3: Find the area of an equilateral triangle whose perimeter is .

Answer:

Perimeter

Therefore side (since triangle is equilateral triangle)

Therefore

Therefore Area of triangle

Question 4: Find the area of a right-angled triangle if the radius of its circumcircle is and altitude drawn to the hypotenuse is .

Answer:

Radius

Therefore Diameter Base (remember, the angle subtended by the diameter on any point on the circumference is a right angle)

Therefore Area of triangle

Question 5: Find the area of a right-angled triangle if the diameter of its circumcircle is and altitude drawn to the hypotenuse is long.

Answer:

Diameter Base

Therefore Area of triangle

Question 6: The perimeter of a right triangle is . Its hypotenuse is . Find the other two sides and the area of the triangle.

Answer:

Perimeter of triangle

Given hypotenuse . Let one side be , then the other side would be

Applying Pythagoras theorem we get

When , the other side is . Similarly, when the other side

Therefore the sides are , and .

Therefore the area of the triangle

Question 7: The cost of turfing a triangular field at the rate of per is . Find the height, if double the base of the triangle is times the height.

Answer:

Let the base Base

The rate of turfing per

Total Cost of turfing

Therefore

Therefore Height

Question 8: The base of a triangular field is three times its height. If the cost of cultivating the field at per hectare is , find its base and height.

Answer:

Let the Height

Therefore the Base

Therefore Area of triangle

1 hectare

Therefore cost of cultivation

Therefore $latex = 486 $

Hence the Base

Question 9: An isosceles right triangle has area . what is the length of its hypotenuse?

Answer:

Let the Base and Height of the isosceles right triangle

Therefore

Therefore hypotenuse or

Question 10: Find the base of an isosceles triangle whose area is and the length of one of its equal sides is .

Answer:

Area

Therefore

Hence

or

and or

Hence is either or

Therefore Base is either or

Question 11: The perimeter of an isosceles triangle is . The base is two-third of the sum of equal sides. Find the length of each side.

Answer:

Perimeter

Let the two equal sides be

Given:

Therefore

Therefore sides are , and

Question 12: Find the area of an isosceles triangle whose equal sides are each and the perimeter is .

Answer:

Therefore

Therefore area

Question 13: Find the area of an isosceles triangle whose base is and perimeter is .

Answer:

Perimeter

Therefore

Therefore

Therefore Area

Question 14: The sides of a right triangle containing the right angle and . Calculate the length of the hypotenuse of the triangle, if its area is .

Answer:

Area

Therefore

(this is not possible as is positive)

Therefore sides are

Hence Hypotenuse

Question 15: is a right triangle right angled at . lf , and area of is 60 \ cm^2 $, find its perimeter.

Answer:

Area

Therefore

(this is not possible as is positive)

Therefore sides are and

Hence Hypotenuse

and Perimeter

Question 16: In the adjoining figure, is an equilateral triangle with each side of length . is a point inside such that and . Find the area of the shaded region.

Answer:

Height of equilateral triangle

Therefore are of equilateral triangle

Height of right angle triangle

Therefore are of right triangle

Therefore shaded area

Question 17: If the difference between the two sides of a right-angled triangle is and the area of the triangle is , find the perimeter of the triangle.

Answer:

Area

Therefore

or (this is not possible as is positive)

Therefore sides are and

Therefore Hypotenuse

Hence Perimeter