find the area of enclosed by each of the figures
Answers
Solution :
For the first figure ABCDE
ABCD is a square with AB = BC = CD = DA = 4 cm
∆ ABC is an equilateral triangle with AC = 4 cm and perpendicular from the vertex B = 2 cm
Area of the square :
=> 16 cm²
Area of ∆ ABC ::
=> ½ × 4 cm × 2 cm²
=> 4 cm²
Total area :
=> 16 cm² + 4 cm²
=> 20 cm²
In the figure (ii) ;
Divide the figure by drawing into two parts through CF
This forms a square CHGF and a trapezium CDEF
Area of the trapezium :
=> ½ × [ Sum of parallel sides ] × [ Distance between them ]
=> ½ × [ FC + DE ] × [ Perpendicular ]
=> ½ × [ 25 cm ] × [ 8 cm ]
=> 100 cm²
Area of the adjacent square :
=> 18 × 18
=> 324 cm²
Total area :
=> 424 cm ²
In the 3rd figure :
This can be again segmented as a trapezium , AFED and a rectangle ABCD
Area of the rectangle :
=> 20 × 15 cm²
=> 300 cm²
Area of the trapezium :
=> ½ × [ 21 ] × 8
=> 21 × 4
=> 84 cm²
Total area :
=> 384 cm²
This is the required answer.
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