Answer:
The area of the polygon is 64 units²
Explanation:
* Lets explain how to solve the problem
- The polygon has 5 sides and 5 vertices
- To find its area by easy way split it into two trapezoid by a horizontal
line y = 1
- The vertices of trapezoid (1) are (-5 , 1) , (4 , 1) , (-5 , 5) , (0 , 5)
- The vertices of one of the parallel bases are (-5 , 1) , (4 , 1)
- The length of this base = 4 - (-5) = 4 + 5 = 9 units
- The vertices of the other parallel bases are (-5 , 5) , (0 , 5)
- The length of this base = 0 - (-5) = 0 + 5 = 5 units
- The length of its height = 5 - 1 = 4 units
- The area of the trapezoid = 1/2 (b1 + b2) × h
∴ Area of trapezoid 1 = 1/2 (9 + 5) × 4 = 28 units²
- The vertices of trapezoid (2) are (4 , 1) , (-5 , 1) , (-5 , -5) , (-2 , -5)
- The vertices of one of the parallel bases are (4 , 1) , (-5 , 1)
- The length of this base = 4 - (-5) = 4 + 5 = 9 units
- The vertices of the other parallel bases are (-5 , -5) , (-2 , -5)
- The length of this base = (-2) - (-5) = -2 + 5 = 3 units
- The length of its height = 1 - (-5) = 1 + 5 = 6 units
∴ Area of trapezoid 1 = 1/2 (9 + 3) × 6 = 36 units²
∵ Area of the polygon = Area trapezoid (1) + Area trapezoid (2)
∵ Area trapezoid (1) = 28 units²
∵ Area trapezoid (2) = 36 units²
∴ Area of polygon = 28 + 36 = 64 units²
∴ The area of the polygon is 64 units²