Herons Formula-Important Questions

1.   Find the area of a right-angled triangle whose base is 12 cm and height is 5 cm.

2.   Find the area of an equilateral triangle with side 10 cm.

3.   Find the area of an isoscles triangle with two equal sides as 5 cm each and the third side as 8 cm.

4.   A triangular park has sides 120 m, 80 m and 50 m. A gardener has to put a fence all around it and also plant grass inside. How much area does he need to plant? Find the cost of fencing it with barbed wire at the rate of Rs. 20 per metre, leaving a space of 3 m wide for a gate on one side.

5.   The sides of a triangular plot are in the ratio of 6 : 7 : 8 and its perimeter is 420 m. Find its area.

6.   A farmer has a triangular field with sides 240 m, 200 m and 360 m, where he grew wheat. In another triangular field with sides 240 m, 320 m and 400 m adjacent to the previous field, he wanted to grow potatoes and onions (see figure). He divided the field into two parts by joining the mid point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions?

       Now 10,000 m² = 1 hectare

7.   Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA; while the other through AC, CD and DA (see figure). Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and LB = 90�, Which group cleaned more area and by how much? Find the total area cleaned by the students (neglecting the width of the lanes).

8.   Parul has a piece of land which is in the shape of a rhombus (see fig.) She wants her daughter and son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonal is 160 m, how much area each of them will get for their crops?

9.   Find the height of a trapezium in which parallel sides are 25 cm 77 cm and non-parallel sides and 26 cm and 60 cm. Given the area of the trapezium as 1644 cm².

10.   What is the area of an equilateral triangle whose side is 2 cm?