B5: Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems.

More simply put: Find strategies to solve simple problems about some kind of measurment that can be used no matter how difficult the problem is.


Problem 1: If a rectangle has a base of 5 cm and a height of 4 cm, what is the area of the rectangle?

Work: To find the area of a rectangle, you must multiply the base length by the length of the height. So, in this case you need to multiply 5 cm by 4cm, which is 20. Area is always expressed in the units you have measured squared.

Answer: 20 sq.cm.

However, depending on what type of figure you are measuring the formula for finding its area would change.


Formulas for Finding Area in Different 2-d Figures: (b=base h= height a=area)

Square: Multpiply one of its dimensions by itself once. (d=dimension)
a=d×d

Triangle: Multiply the base by the height,and then divide that product by 2.
a=bh÷2

Trapezoid: FInd the average of the bases, then multiply that by the height
a=b#1+b#2÷2xh

Circle: Find the radius of the circle. Square that number and then multiply that product ,of that equation by pie. (r =radius)
a= r×r×3.14





Now that you have learned how to find the area in various 2-d shapes ,you can now apply these concepts to find the area of incresingly complex shapes that involve all of these figures.



complicated_shape.jpg
Finding the area of this shape is very simple, you just must simply use what you have already learned about finding the area of individual shapes to find the area of this much more complicated example.
First, begin by finding the area of the main rectangle, excluding the added on shapes. So if you add the lengths of the top and bottem, the length is 18cm. The lengths of the sides are 17cm. You know the formula for finding the area of a rectangle is base times height, so the answer would be 306 .cm sq.
Now you need to add on the other shapes. Well, you do need to worry about the triangles because they are congruent and would cancel one another out. So now find the area of the square. Multiply the dimensions, 4cm and 4cm together, and you will get 16. Next the trapezoid multiply the base and height (7x2) and divide by two which will give you 7sq. cm. And now the circle. To find the area multiply the radius by itself,and multiply that product by 3.14 (4x4x3.14) the answer is 50.24. But, it only shows half of a circle, so you need to divide by two, which gives you 25.12 sq. cm. Now add these amounts together and add them to the other total.



Answer: 354.12 sq.cm