with the vertices A, B and C of a triangle ABC as centre arcs are drawn with radii 5 cm each as shown in the given figure If AB = 14 cm BC =48cm and CA = 50 cm then find the area of the shaded region( use pie = 3.14)
Answers
Answer:
39.25 cm²
Step-by-step explanation:
with the vertices A, B and C of a triangle ABC as centre arcs are drawn with radii 5 cm each as shown in the given figure If AB = 14 cm BC =48cm and CA = 50 cm then find the area of the shaded region( use pie = 3.14)
Three arcs are drawn from points A , B & C with radius = 5 cm
Area of Arc Segment = (segment Angle/360°) * π * Radius²
Area of arc From vertices A = (∠A/360°) * π * Radius²
Area of arc From vertices B = (∠B/360°) * π * Radius²
Area of arc From vertices C = (∠C/360°) * π * Radius²
Sum of Arc Areas = ((∠A+∠B+∠C)/360°) * π * Radius²
∠A+∠B+∠C = 180° (sum of angles of Triangle = 180°)
Sum of Arc Areas = (180°/360°) * π * Radius²
=> Sum of Arc Areas = (1/2) * 3.14 * 5²
=> Sum of Arc Areas = 1.57 * 25
=> Sum of Arc Areas = 39.25 cm²