Answer:
735 cm²
Step-by-step explanation:
The figure is a trapezium .The area of the triangle section can be calculated using the Heron's formula.
The other part of the figure will be a square of sides 21 cm by 21 cm
Area of the square section
Area = l²
Area = 21* 21 = 441 cm²
Area of the triangle using Heron's formula
Sides of the triangle are ;
a= 28 cm
c= 35 cm
b = 21 cm -----height of the trapezium
The Heron's formula is given as;
[tex]A=\sqrt{s( s-a)(s-b )(s-c )}[/tex]
where s is half the perimeter of the triangle
Perimeter of the triangle is given as ;
P= 35 + 28 + 21 =84 cm
s= 84/2 = 42 cm
[tex]A=\sqrt{42*(42-21 )*(42-35 )*(42-28 )} \\\\A=\sqrt{42*(21 )*(7 )*( 14)} \\\\A=\sqrt{86436} \\\\A=294\\\\[/tex]
Total area = 294 + 441 = 735 cm²
