Question

The sides of a triangle are 3 cm, 4 cm and 5 cm What is the area $\left(inc{m}^2\right)$ of a triangle formed by joining the midpoints of this triangle?

• A. $1c{m}^2$
• B. $2.5c{m}^2$
• C. $2c{m}^2$
• D. $1.5c{m}^2$

Answer 1

The correct option is D $1.5c{m}^2$

ABC is the given triangle PQR is the triangle formed by joining the midpoints of $\Delta ABC$
Area of .$\Delta PQR=\frac{1}{4}\left(Areaof\Delta ABC\right)$
For area of $\Delta ABC$ $s=\frac{a+b+c}{2}=\frac{3cm+4cm+5cm}{2}=6cm$

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{6(6-3)(6-4)(6-5)}$$c{m}^2$

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

=$\sqrt{36}c{m}^2=6c{m}^2$

$\therefore$ Area of PQR = $\frac{1}{4}\times 6c{m}^2$ = 1.5 $c{m}^2$