Problem on parallelogram, Finding Area of parallelogram

Geometry construction section in math consists of geometrical figures like parallelogram rectangle, trapezium where we find few terms like linear pair, supplementry angles.
If a pair of angles are adjacent as well as supplementary then they are said to form a linear pair

Topic : Area of parallelogram

Below example also prove how the necessary statements are considered.

Question : In the following figure, NDBA is a rectangle, AN = NG, BF = DB, GD = 11, and DF = 8√2. What is the area of parallelogram GDFA?

State all the statements that are necessary in your proof along with their reasons in a two-column table.

Solution :

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Question on Integrating a Given Function

Here is a Multi choice question to Evaluate function by Integration.
You can find similar set of questions at TutorVista Blogs.

Topic : Integrating a Function.

Below example will help you to identify correct choice and get reasons for, why remaining choices are incorrect.

Question : At what point in the interval [0, √3] does the function y=x² - 1 assumes its average value.
a. -1
b. 1
c. 1.5
d. 1.7

Solution :
Choice b is correct.
Average value = 1/(√3 - 0)₀∫^√3 (x² - 1)dx = 0
And x² – 1 = 0
Therefore, y= x² -1 assumes its average at x = 1

Choice a is incorrect as -1 is not in the interval [0, √3]

Choice c is incorrect as 1.5 does not satisfy the equation x² -1=0

Choice d is incorrect as 1.7 does not satisfy the equation x² -1=0


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