Heron’s Formula Maths - Heron’s Formula

Write the correct answer in the following:
The edges of a triangular board are 6cm, 8cm and 10cm. The cost of painting it at the rate of 9 paise per cm² is:

1. Rs. 2.00
2. Rs. 2.16
3. Rs. 2.48
4. Rs. 3.00

Write True or False and justify your answer:
If the side of a rhombus is 10cm and one diagonal is 16cm, the area of the rhombus is 96cm².

Write True or False and justify your answer:
The area of a triangle with base 4cm and height 6cm is 24cm²

Find the cost of laying grass in a triangular field of sides 50m, 65m and 65m at the rate of Rs. 7 per m².

The area of a trapezium is 475cm² and the height is 19cm. Find the lengths of its two parallel sides if one side is 4cm greater than the other.

A rectangular plot is given for constructing a house, having a measurement of 40m long and 15m in the front. According to the laws, a minimum of 3m, wide space should be left in the front and back each and 2m wide space on each of other sides. Find the largest area where house can be constructed.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13m, 14m and 15m. The advertisements yield an earning of Rs. 2000 per m² a year. A company hired one of its walls for 6 months. How much rent did it pay?

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14cm, 10cm and 6cm. Find the area of the triangle.

A rhombus shaped sheet with perimeter 40cm and one diagonal 12cm, is painted on both sides at the rate of Rs. 5 per m². Find the cost of painting.

The perimeter of a triangle is 50cm. One side of a triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side. Find the area of the triangle.

The sides of a quadrilateral ABCD are 6cm, 8cm, 12cm and 14cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.

A design is made on a rectangular tile of dimensions 50cm × 70cm as shown in the design shows 8 triangles, each of sides 26cm, 17cm and 25cm. Find the total area of the design and the remaining area of the tile.

A field is in the shape of a trapezium having parallel sides 90m and 30m. These sides meet the third side at right angles. The length of the fourth side is 100m. If it costs Rs. 4 to plough 1m² of the field, find the total cost of ploughing the field.

How much paper of each shade is needed to make a kite given in which ABCD is a square with diagonal 44cm.