Two-Dimensional Shapes

2D Shapes and Formulas

Two-dimensional shapes (2D for short) are flat. Most 2D shapes are polygons meaning they have straight lines. For 2D shapes, you will need to know several formulas involving area, perimeter, and circumference.

To find the sum of the interior angles for polygons, use the equation:

180 (n – 2) = sum of the interior angles

Example: Curt wants to know the sum of interior angles for a triangle. N represents the number of sides in the polygon so plug in 3 for the triangle. The sum of the interior angles for an triangle is 180°.

180 (3 -2) = 180°

Circles

A circle has no straight sides, unlike other shapes; therefore, circles are not polygons. You could a draw lines from any point on the circle to the center and all of the lines would have an equal length. These lines are called radii(radius is the singular form.) A line passing through the center from one side to the other is the diameter.

Find the Area of a Circle

Area is concerned with the inside of a circle. The formula reads area is equal to pi multiplied by radius squared. Although pi is actually several trillion digits, for the purpose of this formula, pi always equals 3.14.

Find the area of a circle that has a radius of 10 feet.

Find the Circumference of a Circle

Just like in the area formula, π equals 3.14. The diameter is the radius multiplied by 2. In some questions, you might be given the diameter or you might just be given the radius so don’t make the mistake of squaring the radius in a circumference question.

Find the circumference of a circle that has a 10 foot radius.

Quadrilaterals

Quadrilaterals are four-sided, four-angled polygons. Note the prefix “quad” meaning four. Look at the different types of quadrilaterals below. Notice that sides and angles mirror each other. Let’s take the square for example. Each angle is 90°. There are four angles and 90 multiplied by 4 is 360°. This same concept can be applied to any quadrilateral. Therefore, all quadrilaterals’ interior angles sum to 360°.

Find the Area and Perimeter of a Square (or Rhombus)

Find the Area and Perimeter of a Rectangle (or Parallelogram)

Note: For Parallelogram, the formula is stated as base and height rather than length and width, but is worked the same so Area = B * W and Perimeter = 2(B) + 2(H).

Find the Area and Perimeter of a Trapezoid

Triangles

Triangles are three-sided, three-angled polygons. The sum of a triangle’s interior angles is 180°. Note the prefix “tri” meaning three. There are six types of triangles you might see on the HiSet. Equilateral triangles has three equal sides and angles. Right triangles have one 90° angle. The hypotenuse is the side opposite the right angle. An acutetriangle’s interior angles are each 60°. An obtuse angle has one angle greater than 90°, which means the other two angles must be less than 90°. The isosceles triangle has two equal sides and angles, while a scalene triangle has no equal sides or angles.

Find the Area and Perimeter of a Triangle

---