Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 5 Measurement
Problem
Solution
1) How much carpeting is needed to cover the floor of an L shaped room with the dimensions shown in the figure?
 The long vertical side is 18 ft and the long horizontal side is 22 ft.
Method 1: Cut the figure into two rectangles,
    cutting horizontally, the two rectangles are
    22 x 7 = 154 sq. ft. and 11 x 10 = 110 sq. ft.
    154 sq. ft. + 110 sq. ft. = 264 sq. ft.





Method 2: Cutting vertically,
    the two rectangles are
    10 x 18 = 180 sq. ft. and 12 x 7 = 84 sq. ft.
    180 sq. ft. + 84 sq. ft. =
    264 sq. ft.



Method 3: Use area subtraction:
Complete the outer rectangle, determine it's area and then subtract the 11 x 12 missing rectangle.
    Outer rectangle = 18 x 22 = 396 sq. ft.
    Inner missing rectangle = 11 x 12 = 132 sq. ft.
    Area = 396 - 132 = 264 sq. ft.

Method 4: Use 2 trapezoids!
    Area of a trapezoid = (b1 + b2) h / 2
    A1 = (12+22) x 7 / 2 = 119 sq. ft.
    A2 = (11+18) x 10 / 2 = 145 sq. ft.
    Total area = 264 sq. ft.

Problem
Solution
2) The right triangle BAC has a base of 4 centimeters and a height of 5 centimeters. A new triangle is created by increasing the angle at A by 60o and moving point C to point D. AD has the same length as AC. What is the sum of the angles DBA and BDA in triangle BAD?
1. The new (larger) angle at A is
    90o + 60o = 150 o
2. The sum of the angles of a triangle is 180o
3. The angles DBA and BDA form the other two angles of the triangle with the above 3rd angle at A, so their sum is
    180 - 150 = 30o
    Notice that you don't need the values of angles DBA or BDA.
    You only need their sum.
3) A loop of rope has a total length of 30 feet. Stevie creates a rectangle with the loop that has length 8 ft. Taneisha takes the loop and creates a rectangle that has length 10 ft. What is the difference in the area between Stevie's and Taneisha's rectangle? 1. If Stevie's rectangle has a side 8 ft, then with a perimeter of 30 ft the other (shorter) side is
    (30 - 8 x 2 )/ 2 = 7 ft.
2. If Taneisha's rectangle has a side 10 ft, then with a perimeter of 30 ft the other (shorter) side is
    (30 - 10 x 2) / 2 = 5 ft.
3. Area #1 = 8 x 7 = 56 sq. ft.
    Area #2 = 10 x 5 = 50 sq. ft.
    56 - 50 = 6 sq. ft.
4) Tina's walk home from work is 2 miles. After leaving work she walks 1000 feet and stops to get a drink of water. Tina then walks an additional quarter of a mile and gets her mail. How much further does she need to walk? Give your answer in feet. 1 mile = 5280 feet. 1. Tina's total walk in feet is
    5280 x 2 = 10560 ft.
2. Subtract the first walk to get a drink:
    10560 - 1000 = 9560 ft.
3. Compute how many feet are in 1/4 mile:
    5280/4 = 1320 ft.
4. 9560 - 1320 = 8240 ft.
5) Rocks are being put in an empty well at a rate of 5 rocks per second. After one hour and fifteen minutes how many rocks are in the well? 1. The number of seconds in 1 hour and 15 minutes:
    60 x 60 + 15 x 60 = 3600 + 900 = 4500 seconds
2. Multiply this by the number of rocks per second:
    4500 x 5 = 22500 rocks.