EF divides the rectangle ABCD in two equal parts of _____.

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EF divides the rectangle ABCD in two equal parts of _____.

Options:

A .

6 c m^{2}

B .

5 c m^{2}

C .

8 c m^{2}

D .

10 c m^{2}

Answer: Option A
:
A

$E F$ divides the rectangle ABCD into two trapeziums.

Area of trapezium ABFE
$= \frac{1}{2} \times (S u m o f p a r a l l e l s i d e s) \times (D i s t a n c e b e t w e e n t h e m$
$= \frac{1}{2} \times (A E + B F) \times A B$

$= \frac{1}{2} \times (1 + 2) \times 4$

$= \frac{1}{2} \times 3 \times 4 = 6 c m^{2}$

Area of trapezium CDEF $= \frac{1}{2} \times (F C + E D) \times C D$

$= \frac{1}{2} \times (1 + 2) \times 4$

$= \frac{1}{2} \times 3 \times 4 = 6 c m^{2}$

$Area of both the trapeziums are equal.$

$∴$ $E F$ divides the rectangle $A B C D$ in two equal parts and the area of both the parts are $6 c m^{2}$ .

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