Answer: Top Figure:
Area = 117 m^2
Perimeter = 44.85 m
Bottom:
Area = 18 m^2
Perimeter = 32.74 m
Step-by-step explanation:
Top: Draw a perpendicular line from the 15 m left hand segment to the juncture of the 11 and 9,85 meter segments. We now have a rectangle and a right angle triangle.
Rectangle area = (11m)*(9m) = 99m^2
Rectangle area = (1/2)*(4m)*(9m) = 18m^2
Total area = 117 m^2
Bottom:
Calculate the area of the large right angle triangle formed with the dotted lines. First, calculate the length of the dotted line segment formed by the hypotenuse (7m) and the right side (4m) by: x^2 + (4m)^2 = (7m)^2. Length = 5.745 m. Area of large triangle = (1/2)*(9m+5.745m)*(4m) = 29.49 m^2
Now calculate the area of the small triangle, including the dotted lines: (1/2)*(5.745m)*(4m) = 11.49 m^2.
Subtract the small triangle area froim the large to leave the area for only the triangle formed by solid lines: (29.49m^2 - 11.49 m^2) = 18 m^2.
In both cases, the perimeter is the sum of the identified line segments.
(9+11+9.85+15) = 44.85 m
(4+9+5.745+14) = 32.74m