Answer:
4: 321.5cm²
5: Length of fencing = 62.46cm, Area of Yard: 232cm²
6: Area of 1 sign: 3950cm². Paint cans needed: 237
Step-by-step explanation:
4:
Area of Machine = Area of Square - 1/4 Area of Circle taken away
Area of Machine = (20x20) - 1/4(π10²)
Area of Machine = 400 - 1/4(3.14 x 100)
Area of Machine = 400 - 1/4(314)
Area of Machine = 400 - 78.5 = 321.5cm²
5: The perimeter of this figure is the length of fencing needed. The area of the yard can be figured out:
Perimeter: We're missing one side. So what we need to see here, is that the figure has a hidden triangle. Do you see it? its a missing right angle triangle, and we can use the Pythagorean theorem to find the hypotenuse, which is the missing side:
a² + b² = c²
16² + 7² = c²
256 + 49 = c²
305 = c²
c ≅ 17.46cm
now that we know the last dimension of the trapezoid, the Perimeter is known to be 11 + 16 + 18 + 17.46 = 62.46cm
Area = 1/2(b1+b2) x h
Area = 1/2(11 + 18) x 16
Area = 14.5 x 16 = 232cm²
6:
Area of 1 Sign = Area of rectangle + Area of Triangle
Area of 1 Sign = (90x30) + 1/2(50 x 50)
Area of 1 Sign = 2700 + 25x50
Area of 1 Sign = 2700 + 1250 = 3950cm²
.: area of 6 signs will be 6 x 3950 = 23,700cm²
If one can of paint covers 1 squared meter, then it covers 100 squares cm. So it will take 23700/100 = 237 paint cans to cover all 6 signs :)
Hope this helped!
