# Elements of Architecture

## Geometric Shapes in Architecture

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Circles:

A
*
circle
*
is the set of points in a plane equidistant from a fixed point in the plane called the center. The circle receives its name from the center. O is the symbol used to denote a circle.

Several important terms are associated with the circle. A
*
radius
*
of a circle is a line segment which Joins the center to any point on the circle. AB is a radius of circle A.

(figure available in print form)

A
*
chord
*
is a line segment whose endpoints lie on the circle. CD is a chord of circle A. A
*
diameter
*
is a chord which passes through the center of the circle. CE is a diameter of circle A. A
*
secant
*
is a line which intersects a circle in two points. FG is a secant of circle A.

A
*
tangent
*
is a line which lies in the plane of the circle and intersects the circle in exactly one point. EJ is a tangent to circle A. The
*
point of contact
*
is the point at which the tangent intersects the circle. ~ is the point of contact of tangent EJ. The
*
circumference
*
of a circle is the perimeter or distance around the edge of the circle. An
*
arc
*
is a part of the circumference of a circle. EB is an arc of circle A.

If the circumference of any circle is divided by its diameter, the quotient is always approximately 22/7 or 3.14. This special number is represented by the Greek letter pi (). Hence, the circumference of a circle may be expressed as the product of pi and the length of the diameter of the circle. The formula for finding circumference is C = d or C = 2 r. The area of a circle may be expressed as the product of pi and the square of the length of the radius, or A = r2 .

*
Example:
*

Find the circumference and area of a circle whose diameter is 14 inches long.

*
Solution:
*

C = d | A = r2 |

C = 22/7 x 14 | A = 22/7 x 7 x 7 |

C = 44 inches | A = 154 sq. in.. |

*
Suggested Assignment:
*

Write a report on circular houses used in Africa and in the Arctic.

(figure available in print form)

- Exercises:
- 1. Find the circumference and area of a circle whose radius is 5 1/4 feet long.
- 2. In circle X, identify the following parts:

a. RY e. Line ST b. XZ f. Line UV c. YW g. Point R d. ZW h. Point X - (figure available in print form)
- 3. Illustrated below are floor plans of a round house, a square house, and a rectangular house. The perimeter of each one is 66 feet. Find the area of each figure Which of the houses has the greatest number of square feet of living area?
- (figure available in print form)
- 4. Name the geometric figures that you see in the illustration of the door below at the left.
- 5. How many square inches of glass are necessary to fill the window shown below at the right?