Note: If are the sides of the triangle and s is the semi perimeter, then its area if given by . This is Heron’s Formula.

Question 1: Find the area of a triangle whose sides are respectively .

Answer:

Question 2: Find the area of a triangle whose sides are .

Answer:

Question 3: Find the area of a triangle two sides of which are and the perimeter is .

Answer:

Question 4: In a . Find the area of and hence its altitude on .

Answer:

Question 5: The perimeter of a triangular field is and its sides are in the ratio . Find the area of the triangle.

Answer:

Hence the sides are

Question 6: The perimeter of a right triangle is . If its sides are in the ratio . Find the area of the triangle.

Answer:

Hence the sides are

Question 7: The perimeter of a triangular field is . If two of its sides are , find the length of perpendicular on the side of length from the opposite vertex.

Answer:

Question 8: A triangle has sides long. Find its area. Also, find the smallest of its altitudes.

Answer:

Question 9: The lengths of the sides of a triangle are in the ratio and its perimeter is . Find the area of the triangle and the height corresponding to the longest side.

Answer:

Hence the sides are

Question 10: The perimeter of an isosceles triangle is and its base is times each of the equal sides. Find length of each side of the triangle, area of the triangle and the height of the triangle.

Answer:

Hence the sides are

Question 11: Find the area of a quadrilateral is which

Answer:

Area of Area of Area of

Question 12: The sides of a quadrangular field, taken in order are are respectively. The angle contained by the last two sides is a right angle. Find its area.

Answer:

Area of Area of Area of

Question 13: The sides of a quadrilateral, taken in order are meters respectively, and the angle contained by the first two sides is a right angle. Find its area.

Answer:

Area of Area of Area of

Question 14: A park, in the shape of a quadrilateral , has . How much area does it occupy?

Answer:

Area of Area of Area of

Question 15: Two parallel side of a trapezium are and other sides are . Find the area of the trapezium.

Answer:

Area of Area of Area of

Area of

Question 16: Find the area of a rhombus whose perimeter is and one of whose diagonal is .

Answer:

Therefore Side

Area of Area of Area of

Question 17: A rhombus sheet, whose perimeter is and whose one diagonal is long, is painted on both sides at the rate of . Find the cost of painting.

Answer:

Therefore Side

Area of Area of Area of

Therefore cost of painting

Question 18: Find the area of a quadrilateral in which forms an equilateral triangle whose each side is equal to .

Answer:

Area of Area of Area of

Question 19: Find the area of a quadrilateral in which and diagonal .

Answer:

Area of Area of Area of

Question 20: Find the perimeter and area of the quadrilateral in which .

Answer:

Area of Area of Area of

Question 21: The adjacent sides of a parallelogram measures , and the diagonal measures . Find the area of the parallelogram.

Answer:

Area of Area of Area of