Properties of Two-Dimensional Shapes - Trivium Test Prep Online Courses

# Properties of Two-Dimensional Shapes

## Properties of Two-Dimensional Shapes

Two-dimensional objects can be measured in two dimensions (length and width). A plane is a two-dimensional object that extends infinitely in both dimensions.

Polygons are two-dimensional shapes, like triangles and squares, that have three or more straight sides. Regular polygons are polygons with sides that are all equal and angles that are all equal.

#### Circles

A circle is the set of all the points in a plane that are the same distance from a fixed point (called the center). The distance from the center to any point on the circle is the radius. The diameter is the measurement through the center of the circle and touching two points on the edge. The measure of the diameter is twice the measure of the radius.

A sector is the part of the circle formed by two radii (like a pie slice). An arc is the portion of the circle’s circumference that forms the side of a sector.

Because all the points on a circle are equidistant from the center, all the circle’s radii have the same length.

#### Triangles

Triangles have three sides and three interior angles that always sum to 180°.

• A scalene triangle has no equal sides or angles.
• An isosceles triangle has two equal sides and two equal angles (often called base angles).
• In an equilateral triangle, all three sides are equal, and all angles are 60°.

Quadrilaterals have four sides and four angles.

• In a rectangle, each of the four angles measures 90°, and there are two pairs of sides with equal lengths.
• A square also has four 90° angles, and all four of its sides are an equal length.
• A rhombus has four equal sides and two pairs of equal angles.
• A trapezoid has two parallel sides.
• A parallelogram has two pairs of parallel, equal sides.

#### Perimeter and Area

The size of the surface of a two-dimensional object is its area. The distance around a two-dimensional figure is its perimeter, which can be found by adding the lengths of all the sides.

Area and Perimeter of Basic Shapes
Shape
Area
Perimeter
Triangle
A = $$\frac{1}{2}$$bh
P = s1 + s2 + s3
Square
A = s2
P = 4s
Rectangle
A = l × w
P = 2l + 2w
Circle
A = πr2
C = 2πr
Sector
$$A = \frac{x^\circ}{360^\circ}\pi r^{2}$$
$$s = \frac{x^\circ}{360^\circ}2\pi r$$
Variables
b = base
h = height
s = side
l = length
w = width