Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The sides of a triangle are 3 cm, 4 cm and 5 cm. The area (in $\mathrm{cm}^{2}$ ) of the triangle formed by joining the mid-points of the sides of this triangle is
(a). $\frac{3}{4}$
(b)$\frac{3}{2}$
(c)3
(d)6
Answer
Answer (as printed): B
Explanation
Note: If the mid-points of three sides of a triangle are joined, the whole triangle is divided into four triangles of equal area. $$a=3 \mathrm{cm}, b=4 \mathrm{cm} \text { and } c=5 \mathrm{cm} .$$ It is a right-angle triangle with base = 3 cm and height $=4 \mathrm{cm}$. $$\text { ∴ } \quad \text { Its area }=\left(\frac{1}{2} \times 3 \times 4\right) \mathrm{cm}^{2}=6 \mathrm{cm}^{2} .$$ Area of required triangle $=\left(\frac{1}{4} \times 6\right) \mathrm{cm}^{2}=\frac{3}{2} \mathrm{cm}^{2}$.