ABCD is a quadrilateral and let AB-a-AD-b- AC-ma-nb- Then the area of the quadrilateral is

Nbsp; AB=a,AD=b, nbsp; AC=ma+nb BD = nbsp;AD nbsp;AB = nbsp;b nbsp;a Area of quadilateral = 12 |AC×BD| = 12 |(ma+nb )× (b nbsp;a)| Area of q ...

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Standard X

Mathematics

Areas of Combination of Plane Figures

ABCD is a qua...

Question

$A B C D$ is a quadrilateral and let $- - \to A B = \to a, - - \to A D = \to b, - - \to A C = m \to a + n \to b$ . Then the area of the quadrilateral is

(m + n) | \to a \times \to b |

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\frac{1}{2} (m + n) | \to a \times \to b |

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3 (m + n) | \to a \times \to b |

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2 (m + n) | \to a \times \to b |

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Solution

The correct option is B $\frac{1}{2} (m + n) | \to a \times \to b |$
$- - \to A B = \to a, - - \to A D = \to b, - - \to A C = m \to a + n \to b$
$- - \to B D = - - \to A D - - - \to A B = \to b - \to a$
Area of quadilateral $= \frac{1}{2} | - - \to A C \times - - \to B D | = \frac{1}{2} | (m \to a + n \to b) \times (\to b - \to a) |$
Area of quadilateral $= \frac{1}{2} | m (\to a \times \to b) - n (\to b \times \to a) |$
$= \frac{1}{2} (m + n) | \to a \times \to b |$

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Areas of Combination of Plane Figures

Standard X Mathematics

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ABCD is a quadrilateral and let −−→AB=→a,−−→AD=→b,−−→AC=m→a+n→b. Then the area of the quadrilateral is

$A B C D$ is a quadrilateral and let $- - \to A B = \to a, - - \to A D = \to b, - - \to A C = m \to a + n \to b$ . Then the area of the quadrilateral is