Geometry Answers

Problem A.1

The graph below is made of three line segments:

-1 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

y

x

f(x)

g(x)

h(x)

The segments correspond to the following three functions:

f(x) = x − 2, g(x) = p

4 − (x − 6)2 + 2, h(x) = x − 6

Find the total length L of the graph between x = 2 and x = 10.

Show the complete solution An anchor chain is wound around a drum with radius 1.5 ft.If the Drum is rotated through an angle of 250° how far will the anchor be lowered?

A single-lane street, 12 feet wide goes through a semi-circular tunnel with a radius of 10 feet. How high is the tunnel at the edge of each lane?

Identify what single transformation will transform the white regions into the gray regions.

Describe the algorithm of constructing (using a compass and a ruler) a right-angled triangle knowing its hypotenuse and the ratio of its legs being equal to ¾.

Situation:

Suppose you were one of the engineers of the said project and your job was to renovate or improve the walkway, patio, and driveway. After your ocular inspection, you noticed that a rectangular floor measuring (10m by 14m) needed to be fixed. Likewise, your plan is to put brick paves to ensure that the walkway is strong and durable.

Questions:

1. Each piece of brick is square with an edge of 50 cm. How many pieces of brick paves will be needed to cover the rectangular floor that needs fixing?

2. If one bag of adhesive cement for brick paves can cover 10 sq. m, how many bags of adhesive cement will be needed?

3. Make a model to illustrate the situation with appropriate mathematical solutions.

How many sheets of drywall are needed for the walls and ceiling of the cabin that is 28 feet x 36 feet. The standard wall height is 8 feet.  ( Hint there are no interior walls) A sheet of drywall is ½” x 4’ x 8’ 

Calculate the surface area for a wall that measures 10 feet tall and 48 feet long. The wall has 1 window 3 feet by 3 feet, 2 windows 4 feet by 4 feet, 1 window 2 feet by 3 feet and 3 doors 3 feet by 7 feet. 

You just bought a plot of land that measures 50 feet by 100 feet and are going to build a house on the lot. The house measures 30 feet by 48 feet.  How much of the lot will be left after you place the house in the center of the lot

4. How many of the quadrilaterals possible in the previous problem are:

a. Squares?

b. Rectangles?

c. Parallelograms?

d. Trapezoids?

e. Trapezoids that are not parallelograms?