(Continued from above)Properties and important points to remember-
• A trapezoid has one of the parallel sides, as base. It has two legs, which are non-parallel sides.
• The perpendicular distance from one base to the other is defined as altitude. To find it, one base may need to be extended.
• A trapezoid where both legs have same length is called an isosceles trapezoid. In this case both base angles have also the same measure.
• If the legs are also parallel, it has two pairs of parallel sides and it is a parallelogram.
• A line joining the midpoints of the two legs is called median. The median is always parallel to the bases.
• The length of the median is the average length of the bases, and the formula is: (MN +PO)/2.
• In a trapezoid, the median divides it into two smaller trapezoids and each one has is with half the altitude of the original.
• The formula to determine area (A) can be used: A = [(a+b)/2] * h, Here
a, b represents the base lengths and ‘h’ length of the altitude. In other expression the area of a trapezoid equals (altitude* median).
Example 7 : Given- find the area of trapezoid in the figure given below.
Step 1: Referring to the above Trapezoid ABCD, in which one of the side
DC = 15 cm, side AB = 7 cm and height is 10 cm. AB and DC
are parallel.
its area would be: A = [1/2 (b * h)] + [1/2 (b’ * h’)].
Step 2: A = [1/2 (15 * 10) + [1/2 (7 * 10)]
This on simplification gives A = 75 + 35 = 110 cm2
The area of trapezoid is 110 cm2, as the final answer.
Example 8: Given- two sides of a plot measure 32 metres and 24 metres and the angle between them is a perfect right angle. The other two sides measure 25 metres each and the other three are not right angles. Calculate the area of the plot.
Step 1: Collect he given information and complete the diagram:
Step 2: Draw DC perpendicular to BE as shown above.
Step 3: The area of rectangle
ABCD = length * breadth = 25 * 24 = 600
The area of triangle CDE =(1/2) * base * altitude (height) = (1/2)* 7 * 24 = 84
Area of the plot = area of rectangle ABCD + area of triangle CDE
Area of plot = 600 + 84 = 684 m2, as the final answer.
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