Question

Describe the graphical method to find the area of an irregularly shaped plane figures

Answer 1

QUESTION:- Q.5: Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its 54th term?

☆ANSWER☆

Solution: Given A.P. is 3, 15, 27, 39, …

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) d

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.Let nth term be 771.

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.Let nth term be 771.an = a + (n − 1) d

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.Let nth term be 771.an = a + (n − 1) d771 = 3 + (n − 1) 12

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.Let nth term be 771.an = a + (n − 1) d771 = 3 + (n − 1) 12768 = (n − 1) 12

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.Let nth term be 771.an = a + (n − 1) d771 = 3 + (n − 1) 12768 = (n − 1) 12(n − 1) = 64

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.Let nth term be 771.an = a + (n − 1) d771 = 3 + (n − 1) 12768 = (n − 1) 12(n − 1) = 64n = 65

Solution: Given A.P. is 3, 15, 27, 39, …first term, a = 3common difference, d = a2 − a1 = 15 − 3 = 12We know that,an = a + (n − 1) dTherefore,a54 = a + (54 − 1) d= 3 + (53) (12)= 3 + 636 = 639a54 = 639We have to find the term of this A.P. which is 132 more than a54, i.e. 771.Let nth term be 771.an = a + (n − 1) d771 = 3 + (n − 1) 12768 = (n − 1) 12(n − 1) = 64n = 65Therefore, 65th term was 132 more than 54th term.

Answer 2

Answer:

                  Explanation:

To find the area of an irregularly shaped plane figure, we have to use graph paper.

1.Place a piece of paper with an irregular shape on a graph paper and draw its outline.

2.To find the area enclosed by the outline, count the number of squares inside it (M).

3.You will find that some squares lie partially inside the outline.

4.Count a square only if half (p) or more of it (N) lies inside the outline.

5.Finally count the number of squares, that are less than half. Let it be