Answer:
The total area of the figure = 444 cm²
Step-by-step explanation:
- A quadrilateral in which a pair of opposite sides are parallel is called a trapezium.
- If a and b are the length of two parallel sides of a trapezium, and h is the distance between the two parallel sides (height), then the area of the trapezium is given by,
[tex]A=\frac{h}{2} (a+b)[/tex]
Step 1:
The figure shows two trapezium EFDC and CDBA.
Total area of the given figure is the sum of area of the two trapeziums.
Step 2:
Trapezium EFDC has parallel sides and height as:
a = 24 cm (side EF)
b = 15 cm (side DC)
h = 12 cm
∴ Area of trapezium EFDC is,
[tex]A_{(EFDC)} =\frac{h}{2} (EF+DC)[/tex]
[tex]A_{(EFDC)} =\frac{12}{2} (24+15)[/tex]
[tex]A_{(EFDC)} = 234 cm^{2}[/tex]
Step 2:
Trapezium CDBA has parallel sides and height as:
b = 15 cm (side CD)
a = 21 cm (side BA)
h = 10 cm
∴ Area of trapezium CDBA is,
[tex]A_{(CDBA)} =\frac{h}{2} (CD+BA)[/tex]
[tex]A_{(CDBA)} =\frac{10}{2} (15+21)[/tex]
[tex]A_{(CDBA)} = 210 cm^{2}[/tex]
Step 3:
Total area of the given figure = area of trapezium EFDC + area of trapezium CDBA,
[tex]A_{(EFDBAC)} = A_{EFDC} +A_{CDBA}[/tex]
[tex]= 234 + 210[/tex]
[tex]= 444 cm^{2}[/tex]