This one isn't all that hard, once you know how to do it.
First, you need the formulae.
Area of a rectangle = length x width.
Area of a circle = pi r²
Pi is about 3.1415.
Now, the rectangle bit: 5 x 14 = 70 in.²
The circle bits:
1. the big circle: 3.1415 x 7² = 154. Divide by 2, as it's only half the circle: = 76.96.
2. The small circle: 3.1415 x 2.5² = 19.63. Divide by 2 again: 9.817.
All you have to do now is add up your 3 bits:
76.9 + 9.8 + 70 = 156.7. Rounding, as per your question, we get
157.
I hope that's right.