# Mensuration Part 5

Problem 1: The area of a field in the shape of a trapezium measures 1440m2. The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3, the length of the longer parallel sides is?

Solution:

Area of trapezium =$\frac{1}{2}(a+b)\times&space;h$

$1440=\frac{1}{2}\times&space;(5x+3x)\times&space;24$

$1440=\frac{1}{2}\times&space;(8x)\times&space;24$

$x=15$

5x=5*x=75

Problem 2: What would be the cost of building a 7 meters wide garden around a circular field with the diameter equal to 280 meters if the cost per square meter for building the garden is Rs. 21?

Solution:

$\Pi&space;r^{2}-\Pi&space;r^{2}$

$\Pi&space;(147^{2}-140^{2})$

$\frac{22}{7}\times&space;287\times&space;7=6314$

1m———–>21

6341m—–>? 6341*21 = 132594

Problem 3: There is a rectangular plot whose length is 36 meter and breadth is 28 meter. There are two paths middle of the plot and parallel to length and breadth of the plot. The remaining part is lawn whose area is 825 square meter. What is the area of the paths?

Solution:

Area of rectangle = 36*28 = 1008

Given area of lawn = 1008-825 = 183