[tex]\bold{\huge{\orange{\underline{ Solution }}}}[/tex]
Given :-
- We have given one irregular figure which is composed of parallelogram and trapezium
To Find :-
- We have to find the area of the given irregular figure.
Procedure to calculate the area of the given figure :-
- { Firstly, we will find the area of parallelogram and then we will find the area of trapezium. After that, we will add both the areas and hence we got the total area of the given figure }
Let's Begin :-
According to the question,
We have,
- Height of the parallelogram = 5 cm
- Base of the parallelogram 10cm
- Height of the trapezium = 6 cm
- Length of Parallel sides of trapezium = 7cm and 14 cm
Therefore,
We know that,
Area of parallelogram
[tex]\bold{\red{ = Base × Height }}[/tex]
Subsitute the required values,
[tex]\sf{ = 10 × 5 }[/tex]
[tex]\bold{ = 50 \: cm² }[/tex]
Thus, The area of parallelogram is 50 cm²
Now,
Area of trapezium
[tex]\bold{ =}{\bold{\red{\dfrac{1}{2}}}}{\bold{\red{× (a + b) × Height }}}[/tex]
- Here, ( a + b) represents the similarity of parallel sides
Subsitute the required values,
[tex]\sf{ =}{\sf{\dfrac{1}{2}}}{\sf{× (7 + 14) × 6 }}[/tex]
[tex]\sf{ =}{\sf{\dfrac{1}{2}}}{\sf{× 21 × 6 }}[/tex]
[tex]\sf{ = 21 × 3 }[/tex]
[tex]\bold{\pink{ = 63 cm²}}[/tex]
Thus, The area of trapezium is 63 cm²
Now,
The total area of the given figure
[tex]\sf{ = 50 + 63 }[/tex]
[tex]\bold{\green{ = 113 cm²}}[/tex]
Hence, The total area of the given figure is 113 cm² .
