Question 1 :
Find the area of the figure shown below.
Question 2 :
Find the area of the figure shown below.
Question 3 :
John bought a square plot of side 60 m. Adjacent to this David bought a rectangular plot of dimension 70 m x 50 m. Both paid the same amount. Who is benefited ?
Question 4 :
Find the area of the figure shown below.
Question 5 :
Daniel bought a square plot of side 50 m. Adjacent to this Richard bought a rectangular plot of length 60 m and breadth 40 m for the same price. Find out who is benefited and how many sq. m. are more for him ?
1. Answer :
By drawing a line GD parallel to AB, we can split the given picture as two parts.
(i) GDEF is a square of side length 3 cm
(ii) ABCG is a rectangle of length 10 cm and width 4 cm
Area of square = a^{2}
Area of rectangle = length x breadth
Area of square (GDEF) = 3^{2} = 9 cm^{2}
Area of rectangle = 10 x 4 = 40 cm^{2}
Area of the given figure = 40 + 9 = 49 cm^{2}
2. Answer :
By drawing a line BD parallel to AE, we can split the given picture as two parts.
(i) BCD is a triangle
(ii) ABED is a rectangle
Area of triangle = (1/2) x b x h
Area of rectangle = length x breadth
Length of AC = 17
AB + BC = 17 -----> 10 + BC = 17 -----> BC = 7 cm
Area of triangle = (1/2) x 7 x 5 = 35/2 = 17.5 cm^{2}
Area of rectangle = 10 x 5 = 50 cm^{2}
Area of given shape = 17.5 + 50 = 67.5 cm^{2}
3. Answer :
To find who is benefited, we have to find the area of above shapes separately.
(i) ABFG is a square of side length 60 m
(ii) BCDE is a rectangle of length 70 m and width 50 m.
Area of square = a^{2}
Area of rectangle = length x breadth
Area of ABFG = 60^{2} = 60 x 60 = 3600 m^{2}
Area of rectangle = 70 x 50 = 3500 m^{2}
From the above calculation, we come to know that John is having more area than David. So John is more benefited.
4. Answer :
(i) ABCD is a square of side length 15 cm
(ii) Area of rectangle FEGH
Length of DC = 15
DF + FE + EC = 15 -----> 3 + FE + 5 = 15
FE = 15 - 8 -----> FE = 7 cm
Area of square (ABCD) = a^{2} = 15^{2} = 225 cm^{2}
Area of rectangle (FEGH) = length x width
= 20 x 7
= 140 cm^{2}
Area of the given figure = 225 + 140 = 365 cm^{2}
5. Answer :
Area of land owned by Daniel = a^{2}
= 50^{2}
= 50 x 50
= 2500 m^{2}
Area of land owned by Richard = length x width
= 60 x 40
= 2400 m^{2}
Because Daniel is having more area than Richard, we can decide that Daniel is benefited.
Daniel is having 100 m^{2} more area than Richard.
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