Question

The sides of triangles are 10cm, 24cm, and 26cm. At each vertex of the triangle, circles of radius 3cm are drawn. What is the area of the triangle in sqcm, excluding the portion enclosed by circles? $(\pi=3.14)$.

• A. 105.87
• B. 110
• C. 126.6
• D. 114

Answer 1

Answer:

A. 105.87

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

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

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

$Radius,r=3cm$

Base b= 24., height h=10cm

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{24}\times{10}-\frac{1}{2}\times{3.14\times{3\times{3}}}

=>\frac{1}{2}[240-28.26]

=>105.87