Important Note :
1. Perimeter of a square .
2. Perimeter of a rectangle
3. Circumference of a circle
4. Circumference of a semi circle
5. Perimeter of a rhombus
6. Perimeter of a parallelogram .
7. Area of a square .
8. Area of a rectangle .
9. Area of a circle
10. Area of a semi circle
11. Area of a rhombus
12. Perimeter of a triangle the Sum of three sides of a triangle .
13. Perimeter of equilateral triangle
14. Area of a right angles triangle
15. Area of a equilateral triangle
16. Area of a triangle ,where are the sides of the triangle and
Semi perimeter .
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Solution: Since is the side of an equilateral triangle .
So, the perimeter of an equilateral triangle is .
The semi-perimeter of an equilateral triangle
The area of the signal board
Second part : Given, the perimeter
The area of the signal board
Solution : Here, , ,
The area of the one triangular wall
The area of two triangular wall
The rent pay by company
Solution : Here, , and
The area of the triangle wall
Solution: let be the third side of the triangle .
Here, , and
The area of the triangle
Solution : Let , and are the sides of the triangle .
Here, , , and
and
So , , and
The area of the triangle
Solution : let be the third side of an isosceles triangle .
Again ,
Here, , , and
The area of the triangle
1. A park, in the shape of a quadrilateral ABCD, has , AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?
2. Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
3. Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used. Fig. 12.15
4. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
5. A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
6. An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig. 12.16), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17. How much paper of each shade has been used in it? Fig. 12.16 Fig. 12.17
8. A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per .
9. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.