Answer:
Area = 30 , Perimeter = 22.31 ⇒ Answer (B)
Explanation:
* Lets study the figure
- The length of AE = 5
- The length of DC = 3
- The length of BC = 4
- Tho find the length of DE and AB we must use Pythagoras Theorem
∵ The vertical distance of ED = 3 and the horizontal distance = 2
∴ ED = √(3² + 2²) = √13
- Similar we will find AB
∵ The vertical distance of AB = 6 and the horizontal distance = 3
∴ AB = √(6² + 3²) = √45
* Now we can find its perimeter
- The perimeter = 5 + 4 + 3 + √13 + √45 = 22.31
* to find the area we will divided it into 2 trapezium
- The first one contains E , D , C with point of intersection
between the vertical axis with side CB
- The lengths of its 2 parallel bases are 3 , 6 and height 2
- The second one contains E , A , B with point of intersection
between the vertical axis with side BC
- The lengths of its 2 parallel bases are 2 , 5 and height 6
∵ Area trapezium = (1/2)(b1 + b2) × h
- The area of 1st one = (1/2)(3 + 6) × 2 = 9 units²
- The area of 2nd one = (1/2)(2 + 5) × 6 = 21 units²
∴ The area of the figure = 9 + 21 = 30 units²
* Area = 30 , Perimeter = 22.31