In the figure, ABC is a equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of equal radius. Find the area of the shaded region correct upto 2 decimal places. Take pie = 3.142 and underoot 3 = 1.732.
Answers
Answer:
2.576 cm²
Step-by-step explanation:
Since this is an Equilateral triangle the angles of the triangle are each 60°.
The corners form sectors of a circle.
When we join the sectors we form a major sector with the middle angle as (60 × 3) = 180°
Area of the shaded region = Area of the triangle - area of the sector.
Area of the triangle = 1/2 × base × height
We need to get the height of the triangle using Pythagoras theorem :
Base = 8/2 = 4 cm
Hypotenuse = 8 cm
Height = square root of (8² - 4²)
= Square root (16 × 3) = 4 × root 3
Root 3 = 1.732
Square root 48 = 4 × 1.732 = 6.928 cm
Area of the triangle = 1/2 × 6.928 × 8 = 27.712 cm²
Area of the Sector :
Radius of the sector = 8/2 = 4 cm
Area of the sector = 180/360 × 3.142 × 4² = 25.136 cm²
Area of the shaded region = 27.712 - 25.136 = 2.576 cm²
Step-by-step explanation:
your answer is 2.576 and correct upto two decimal place is 2.58
