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- Perimeter of the semicircle + Diameter of the circle
= {tex}\pi (\frac{2.8}{2}){/tex} cm + 2.8 cm
= {tex}\frac{22}{7} \times{/tex} 1.4 cm + 2.8 cm
= 4.4 cm + 2.8 cm
= 7.2 cm - Perimeter of the 3 sides of rectangle + Perimeter of semicircle
= 2.8 cm + 1.5 cm + 1.5 cm + {tex}\pi (\frac{2.8}{2}){/tex} cm
= 5.8 cm + {tex}\frac{22}{7} \times{/tex} 1.4 cm
= 5.8 cm + 4.4 cm
= 10.2 cm - Perimeter of semicircle + Perimeter of 2 sides of the triangle
= 2 cm + 2 cm + {tex}\pi (\frac{2.8}{2}){/tex} cm
= 4 cm + {tex}\frac{22}{7} \times{/tex} 1.4 cm
= 4 cm + 4.4 cm
= 8.4 cm
Therefore, the ant would have to take a longer round for food pieces (b).
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Mensuration is the branch of mathematics which deals with the study of Geometric shapes, their area, volume and related parameters.
Some important mensuration formulas are:
1. Area of rectangle (A) = length(l) × Breath(b)
2. Perimeter of a rectangle (P) = 2 × (Length(l) + Breath(b))
3. Area of a square (A) = Length (l) × Length (l)
4. Perimeter of a square (P) = 4 × Length (l)
5. Area of a parallelogram(A) = Length(l) × Height(h)
6. Perimeter of a parallelogram (P) = 2 × (length(l) + Breadth(b))
7. Area of a triangle (A) = (Base(b) × Height(b)) / 2
And for a triangle with sides measuring “a” , “b” and “c” , Perimeter = a+b+c
and s = semi perimeter = perimeter / 2 = (a+b+c)/2
And also: Area of triangle =
This formulas is also knows as “Heron’s formula”.
8. Area of triangle(A) =
Where A, B and C are the vertex and angle A , B , C are respective angles of triangles and a , b , c are the respective opposite sides of the angles as shown in figure below:
area of triangle - mensuration
9. Area of isosceles triangle =
Where a = length of two equal side , b= length of base of isosceles triangle.
10. Area of trapezium (A) =
Where “a” and “b” are the length of parallel sides and “h” is the perpendicular distance between “a” and “b” .
11. Perimeter of a trapezium (P) = sum of all sides
12. Area of rhombus (A) = Product of diagonals / 2
13. Perimeter of a rhombus (P) = 4 × l
where l = length of a side
14. Area of quadrilateral (A) = 1/2 × Diagonal × (Sum of offsets)
15. Area of a Kite (A) = 1/2 × product of it’s diagonals
16. Perimeter of a Kite (A) = 2 × Sum on non-adjacent sides
17. Area of a Circle (A) =
Where r = radius of the circle and d = diameter of the circle.
18. Circumference of a Circle =
r= radius of circle
d= diameter of circle
19. Total surface area of cuboid =
where l= length , b=breadth , h=height
20. Total surface area of cuboid =
where l= length
21. length of diagonal of cuboid =
22. length of diagonal of cube =
23. Volume of cuboid = l × b × h
24. Volume of cube = l × l × l
25. Area of base of a cone =
26. Curved surface area of a cone = C =
Where r = radius of base , l = slanting height of cone
27. Total surface area of a cone =
28. Volume of right circular cone =
Where r = radius of base of cone , h= height of the cone (perpendicular to base)
29. Surface area of triangular prism = (P × height) + (2 × area of triangle)
Where p = perimeter of base
30. Surface area of polygonal prism = (Perimeter of base × height ) + (Area of polygonal base × 2)
31. Lateral surface area of prism = Perimeter of base × height
32. Volume of Triangular prism = Area of the triangular base × height
33. Curved surface area of a cylinder =
Where r = radius of base, h = height of cylinder
34. Total surface area of a cylinder =
35. Volume of a cylinder =
36. Surface area of sphere =
where r= radius of sphere, d= diameter of sphere
37. Volume of a sphere =
38. Volume of hollow cylinder =
where , R = radius of cylinder , r= radius of hollow , h = height of cylinder
39. Right Square Pyramid:
If a = length of base , b= length of equal side ; of the isosceles triangle forming the slanting face , as shown in figure:
net diagram of right square pyramid
39.a Surface area of a right square pyramid =
39.b Volume of a right square pyramid =
40. Square Pyramid:
40.a. Johnson Pyramid:
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</dt>
<dd>net diagram of johnson pyramid</dd>
</dl>
Volume =
Total Surface Area:
40.b. Normal Square pyramid:
If a = length of square base and h = height of the pyramid then:
Volume =
Total Surface Area =
41. Area of a regular hexagon =
42. area of equilateral triangle =
43. Curved surface area of a Frustums =
44. Total surface area of a Frustums =
45. Curved surface area of a Hemisphere =
46. Total surface area of a Hemisphere =
47. Volume of a Hemisphere =
48. Area of sector of a circle =
where 
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{tex}\begin{array}{l}x^2+5x+6\\=x^2+3x+2x+6\\=x(x+3)+2(x+3)\\=(x+3)(x+2)\end{array}{/tex}
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Mayank Chaudhary 7 years, 1 month ago
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