Answer:
The length of the bold figure ABCDEFGH is 30.8 units
Explanation:
* To solve the problem look to the attached figure
- There is a square of area 81 units²
∵ The area of the square = L² , where L is the length of the side of
the square
∵ The area of the square = 81 units²
∴ L² = 81 ⇒ take √ for both sides
∴ L = 9 units
- Two points are drawn on each side of a square dividing it into 3
congruent parts
∵ 9 ÷ 3 = 3
∴ The length of each part is 3 units
- Quarter-circle arcs connect the points on adjacent sides to create
the attached figure
∵ The radius of each quarter circle is 3 units
∵ The length of each side joining the two quarter circle is 3 units
∵ The figure ABCDEFGH consists of 4 quarters circle and 4 lines
- The length of the 4 quarters circle = the length of one circle
∵ The length of the circle is 2πr
∴ The length of the 4 quarters circle = 2 π (3) = 6π units
∵ The length of each line = 3 units
∴ The length of the figure = 6π + 4 × 3 = 30.8 units
* The length of the bold figure ABCDEFGH is 30.8 units