is right angled at B. Given that AC = 15 cm, AB = 9 cm and E and … - Vidyadip

MCQ

$\triangle\text{ABC}$ is right angled at $B.$ Given that $AC = 15\ cm, AB = 9\ cm$ and $E$ and $D$ are the mid-points of sides $AC$ and $AB$ res. Calculate the area of $\triangle\text{ADE}.$

A
$12.5\ cm^2$
B
None of these.
✓
$13.5\ cm^2$
D
$11.5\ cm^2$

✓

Answer

Correct option: C.

$13.5\ cm^2$

As $D$ and $E$ are the midpoints of $AB$ and $AC.$
So, by mid-point theorem
$\text{DE} = \frac{\text{BC}}{2} = \frac{12}{2} = 6\text{cm}$
$\text{AD} = \frac{\text{AB}}{2} = \frac{9}{2} = 4.5\text{cm}$
Area of $\triangle\text{ADE} = 0.5 × \text{DE} × \text{AD}$
$= 0.5 × 6 × 4.5 = 13.5\text{cm}^2$

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