Question

Which of the following options can be expressed as the area of given trapezium ABCF?

• A. $\frac{1}{2}$$\times$(AB+CF)$\times$AE
• B. $\frac{1}{2}$$\times$(AB+CF)$\times$BD
• C. AB$\times$AE +
  $\frac{1}{2}$$\times$FE$\times$AE + $\frac{1}{2}$$\times$BD$\times$CD
• D. AB$\times$CF

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\frac{1}{2}$$\times$(AB+CF)$\times$AE
B $\frac{1}{2}$$\times$(AB+CF)$\times$BD
C AB$\times$AE +

$\frac{1}{2}$$\times$FE$\times$AE + $\frac{1}{2}$$\times$BD$\times$CD
Given: AE = BD = Height of trapezium ABCF
Area of ABCF = Area of Trapezium
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$Height
= $\frac{1}{2}$$\times$(AB+CF)$\times$AE
Similarly, as BD is also height of same trapezium
Area of ABCF = Area of Trapezium
= $\frac{1}{2}$$\times$(AB+CF)$\times$BD

Area of ABCF=Area of rectangle ABDE
+ Area of $△$ AEF
+ Area of $△$ BDC
= AB$\times$AE + $\frac{1}{2}$$\times$AE$\times$FE + $\frac{1}{2}$$\times$BD$\times$DC