问题1.具有如图所示测量值的正方形和矩形区域具有相同的周长。哪个领域面积更大?
解决方案：
Given,
Side of a square = 60 m
Length, l = 80 m
According to question,
Perimeter of rectangular field = Perimeter of square field
According to formula,
2(l + b) = 4 × Side
2(80 + b) = 4 × 60
160 + 2b = 240
b = 40
Therefore, Breadth of the rectangle is 40 m.
Now, Area of Square field = (side)2 = (60)2 = 3600 m2
And Area of Rectangular field = length × breadth = 80 × 40 = 3200 m2
Hence, area of square field is larger.
问题2. Kaushik夫人有一个方形图，其尺寸如图所示。她想在地块的中间盖房子。房子周围有一个花园。找出以卢比为单位在房屋周围开发花园的总成本。每平方米2 55。
解决方案：
Given,
Side of a square = 25 m
According to formula,
Area of square plot = square of a side = (side)2 = (25)2 = 625
Therefore, the area of a square plot is 625 m2
Length of the house = 20 m and
Breadth of the house = 15 m
Area of the house = length × breadth = 20 × 15 = 300 m2
Area of garden = Area of square plot – Area of house = 625 – 300 = 325 m2
Therefore, per unit cost of making garden is Rs. 55
Total Cost of developing the garden of 325 sq. m = Rs. 55 × 325 = Rs. 17,875
问题3。花园的形状在中间为矩形，在端部为半圆形，如图所示。找到这个花园的面积和周长[矩形的长度是20 –(3.5 + 3.5米)]
解决方案：
Given,
Total length = 20 m
Diameter of semi circle = 7 m
Therefore, Radius of semi circle = 7/2 = 3.5 m
Length of rectangular field = 20 – (3.5 + 3.5) = 20 – 7 = 13 m
Breadth of the rectangular field = 7 m
Area of rectangular field = l × b = 13 × 7= 91m2
Area of two semi circles = 2 × (1/2) × pi × r2
= 2 × (1/2) × 22/7 × 3.5 × 3.5
= 38.5 m2
Area of garden = 91 + 38.5 = 129.5 m2
Now Perimeter of two semi circles = 2.pi.r = 2 × (22/7) × 3.5 = 22 m
Therefore, Perimeter of garden = 22 + 13 + 13 = 48 m
问题4.地板砖的形状为平行四边形，底部为24厘米，相应的高度为10厘米。覆盖1080 m 2的地板需要多少个这样的瓷砖? [如果需要，您可以按照想要填满角落的任何方式分割瓷砖]
解决方案：
Given,
Base of flooring tile = 24 cm = 0.24 m
Corresponding height of a flooring tile = 10 cm = 0.10 m
Now Area of flooring tile = Base × Altitude = 0.24 × 0.10 = 0.024
Area of flooring tile is 0.024m2
Number of tiles required to cover the floor = Area of floor/Area of one tile = 1080/0.024 = 45000 tiles
Hence 45000 tiles are required to cover the floor.
问题5：一只蚂蚁在散落在地板上的几个不同形状的食物周围移动。蚂蚁必须为哪个食物做更长的回合?请记住，可以使用表达式C = 2.pi.r获得圆的周长，其中r是圆的半径。
解决方案：
(一种)
Radius = Diameter/2 = 2.8/2 cm = 1.4 cm
Circumference of semi-circle = pi.r = (22/7)×1.4 = 4.4
Circumference of semi-circle is 4.4 cm
Total distance covered by the ant = Circumference of semi – circle + Diameter = 4.4 + 2.8 = 7.2 cm
(b)
Diameter of semi-circle = 2.8 cm
Radius = Diameter/2 = 2.8/2 = 1.4 cm
Circumference of semi-circle = r = (22/7) × 1.4 = 4.4 cm
Total distance covered by the ant= 1.5 + 2.8 + 1.5 + 4.4 = 10.2 cm
(C)
Diameter of semi-circle = 2.8 cm
Radius = Diameter/2 = 2.8/2 = 1.4 cm
Circumference of semi-circle = pi.r = (22/7) × 1.4 = 4.4 cm
Total distance covered by the ant = 2 + 2 + 4.4 = 8.4 cm
After analyzing results of three figures, we concluded that for figure (b) food piece, the ant would take a longer round.