Geometry Answers

What is the weight of a steel plate 15 feet long, 4 feet wide, and 5/8 inches

Thick, if the steel weighs 475 lbs/ ft3 .

1. Find the Lateral surface are of the steel plate in square feet.
2. Compute the Total surface area in square feet.

Find the distance, in inches between two vertices of a cube that are farthest 

From each other, if an edge measures 10 inches.

b) Compute the lateral surface area of the cube in square inches.

c) Compute the Total Surface area of the cube in inches squared

d) Compute the volume of the cube in cubic inches.

What is the measure of a median of a trapezoid if the base is 15 and 18?

A reinforcement shape of a triangle ABC with altitude AD= 5.7cm DC=7.6cm and angle B 42 degrees calculate the length of edge AC

All of the previous questions used what we know as Euclidean geometry.

There are other geometries. One such is spherical geometry.

What can you say about the sum of the interior angles of a triangle in spherical geometry?

TOTAL

This question is concerning the completion of the square by using plane geometry

The area of a square of length x is : x

2

The area of a rectangle of sides x and y is : xy

Consider the expression : x

2 + 10x

Such can be considered as the sum of two areas viz square x

2 and a rectangle 10x

Now do the following (sketch essential)

Divide the rectangle into two equal areas viz 5x and 5x

Next to the square place the two rectangles with the side x in common. One to the RHS and the other below.

You will now have a ’nearly complete’ square

a) What is the length of each side of the ’missing square’ in your diagram

b) If you add the area of the missing square to make a big square, what is the area of the complete (big) square

c) By using the areas from your sketch, find the expressions ? and ?? in the following:

x

2 + 10x + (?)2 = (??)2

What is the perimeter of the trapezoid?

Draw a triangle with vertices x(-1,0) y(0,3) z(5,2)

Draw a triangle with vertices x(-1,0) y(0,3)z(5,2)

The distance between the centers of the two gears is 20

cm . The shaft of each gear is 5 cm and 9 cm respectively.

A. What are the central angles of the shafts

on the gears? 

B. What is the length of the arc length part

of the belt? 

C. What is the length of the non-contacting part of the belt? 

D. What is the total length of the belt?