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Area of a Right Triangle

If the area o...

Question

If the area of the rectangle $A B C D = a b$ sq. units, then the area of the triangle $A B C$ is

\frac{1}{2} \times a b

sq. units

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\frac{1}{4} \times a b

sq. units

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\frac{1}{8} \times a b

sq. units

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Solution

The correct option is A $\frac{1}{2} \times a b$ sq. units
For the rectangle $A B C D$ as shown.
Area of $A B C D = a b$ sq. units.
Now, $A C$ is one of the diagonals.
$∴$ Area $Δ A B C = \frac{1}{2} \times Area of ABCD$
$\Rightarrow$ Area $Δ A B C = \frac{1}{2} \times a b$ sq. units

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If the area of the rectangle ABCD=ab sq. units, then the area of the triangle ABC is

The correct option is A 12×ab sq. unitsFor the rectangle ABCD as shown. Area of ABCD=ab sq. units. Now, AC is one of the diagonals. ∴ Area ΔABC=12× Area of ABCD ⇒ Area ΔABC=12×ab sq. units

If the area of the rectangle $A B C D = a b$ sq. units, then the area of the triangle $A B C$ is

The correct option is A $\frac{1}{2} \times a b$ sq. units
For the rectangle $A B C D$ as shown.
Area of $A B C D = a b$ sq. units.
Now, $A C$ is one of the diagonals.
$∴$ Area $Δ A B C = \frac{1}{2} \times Area of ABCD$
$\Rightarrow$ Area $Δ A B C = \frac{1}{2} \times a b$ sq. units