Part A
The yard is a quadrilateral with the following corner points
I'll label those points A through D in the order presented above.
From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.
In short: side AB is 40 feet long.
The length of side BC is not as simple. We'll need the distance formula.

Segment BC is exactly
feet long, which is about 41.2311 feet.
Use the distance formula again to find the distance from point C(40,50) to D(50,0)

Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.
We have these side lengths:
AB = 40
BC = 41.2311 (approximate)
CD = 50.9902 (approximate)
AD = 50
Add up those four sides and we'll get the perimeter of the quadrilateral.
AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213
Answer: About 182.2213 feet
===================================================
Part B
The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).
This 15 by 20 rectangle has an area of 15*20 = 300 square feet.
The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.
The area of the trapezoid is
A = h*(b1+b2)/2
A = 15*(20+35)/2
A = 412.5
That decimal value is exact.
Add it onto the area of the rectangle
412.5+300 = 712.5
Answer: 712.5 square feet exactly