Question

In a figure, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are the mid points of the sides AB and AC respectively, calculate the area of $\Delta$ADE

• A. 13.5 cm${}^2$
• B. 12.5 cm${}^2$
• C. 23.5 cm${}^2$
• D. none of the above

Answer 1

The correct option is A 13.5 cm${}^2$

Given that $AB=9cm,AC=15cm$

$BC=\sqrt{A{C}^2-A{B}^2}$

$BC=\sqrt{{15}^2-9^2}$

$BC=12cm$

$DE$ = $\frac{BC}{2}=\frac{12}{2}=6cm$
D is the mid point of the side AB

AD = $\frac{AB}{2}=\frac{9}{2}=4.5cm$

$Areaof△ADE=\frac{1}{2}\times AD\times DE=\frac{1}{2}\times 4.5\times 6=13.5c{m}^2$