Question

The sides of triangles are 3cm, 4cm, and 5cm. At each vertex of the triangle, circles of radius 6 cm are drawn. What is the area of the triangle in sqcm, excluding the portion enclosed by circles? $(\pi=3.14)$.

• A. 5 sqcm
• B. 8 sqcm
• C. 5.76 sqcm
• D. 5.72 sqcm

Answer 1

Answer:

D. 5.72 sqcm

sides of are triangle values are triplets so it is an right angled triangle.

Area of Remaining portion = Area of $\triangle$ - Area of Sector

Area of Sector = $\frac{\theta}{360^o}\times{\pi{r^2}}$

$Radius, r=1 cm$

Base b= 4., height h=3cm

Area of remaining portion = $\frac{1}{2}{bh}-\frac{\theta_1}{360^o}\times{\pi{r^2}}+\frac{\theta_2}{360^o}\times{\pi{r^2}}+\frac{\theta_3}{360^o}\times{\pi{r^2}}$

=>\frac{1}{2}{bh}-\frac{\pi{r^2}}{360^o}[\theta_1+\theta_2+\theta_3]

Sum of interior angles of an triangle is $180^o$

$Here, \theta_1+\theta_2+\theta_3=180^o$

=>\frac{1}{2}{bh}-\frac{180^o}{360^o}{\pi{r^2}}

=>\frac{1}{2}\times{3}\times{4}-\frac{1}{2}\times{3.14\times{1\times{1}}}

=>\frac{1}{2}[6-3.14]

=>5.72 sqcm