Answer:
- a = 6.5 m
- perimeter = 52 m
Step-by-step explanation:
The shape is a trapezoid on top of a parallelogram. The areas of each of the figures can be found separately, then added together.
Trapezoid area
The area formula is ...
A = 1/2(b1 +b2)h . . . . where b1, b2 are the base lengths and h is the height
A = 1/2(12 +a)(7) = 3.5(12 +a) = 42 +3.5a
__
Parallelogram area
The area formula is ...
A = bh
A = (12)(9) = 108
__
The area of the figure is then ...
total area = trapezoid area + parallelogram area
172.75 = 42 +3.5a + 108
22.75 = 3.5a . . . . . . . . . . . . subtract 150
6.5 = a . . . . . . . . . . divide by 3.5
The length 'a' is 6.5 meters.
__
Perimeter
The perimeter is the sum of the side lengths. Opposite sides of the parallelogram are the same length. Clockwise from the bottom left, the sum of side lengths is ...
P = 9.2 +7.8 +6.5 +7.3 +9.2 +12 . . . meters
P = 52 . . . meters
The perimeter is 52 meters.
