The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.
Step-by-step explanation:
The given is,
Dimensions of square has length of 10 cm
Trapezoid has base lengths of 8 cm and 14 cm
The length of the trapezoid is 4 cm
Rectangle has side length of 20 cm and 6 cm
Step:1
Area of composite figure = Area of square + Area of Trapezoid
+ Area of rectangle.......................(1)
Step:2
Formula for area of square,
[tex]A_{square} = a^{2}[/tex]
where, a - side of length = 10 cm
[tex]=10^{2}[/tex]
[tex]=100[/tex]
Area of square, [tex]A_{square}[/tex] = 100 Square centimeter
Step:3
Formula for area of Trapezoid,
[tex]A_{Trapezoid}[/tex] = [tex]\frac{a+b}{2} h[/tex].......................................(2)
Where, a - 8 cm
b - 14 cm
h - 4 cm
From equation (2)
= [tex]\frac{8+14}{2} 4[/tex]
= [tex](11)(4)[/tex]
= 44
Area of Trapezoid, [tex]A_{Trapezoid}[/tex] = 44 square centimeters
Step:4
Formula for area of rectangle,
[tex]A_{Rectangle} =lb[/tex]......................................(3)
Where, l = 20 cm
b = 6 cm
Equation (3) becomes,
[tex]= (20)(6)[/tex]
= 120
Area of rectangle, [tex]A_{Rectangle}[/tex] = 120 square centimeters
Step:5
From Equation (1),
[tex]A_{Composite}[/tex] = 100 + 44 + 120
= 264 square centimeters
Result:
The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.
Answer: b)
The area of the composite figure is 264 square centimetres, if a composite figure comprised of a square, trapezoid and a rectangle.
