DEVELOPING FORMULAS FOR TRIANGLES AND QUADRILATERALS Geometry H2 (Holt 10-1)K. Santos.

DEVELOPING FORMULAS FOR TRIANGLES AND QUADRILATERALS

Geometry H2 (Holt 10-1) K. Santos

Area of a Parallelogram

Area = product of its base and height

A= bh Base must be perpendicular to the height

b

h

5cm 3cm

9cm

Example

Find the perimeter of a parallelogram, in which the base is 4ft and the area is 12 .

Area of a Triangle

Area = one half of the product of its base and height

A= bh or A = Base perpendicular to height

h h h

b b b

If b = 4” and h = 6”

Example—finding a side

The area of a triangle is 24 and its height is 3 cm. Find the length of its corresponding base.

Area of a Trapezoid

Area = (average of the bases)(height)

A = h

h

Remember: height is perpendicular to both bases

Example 1--Trapezoid

Find the area of the trapezoid. 20 in 25 in

18 in36 in

Example 2--Trapezoid

Find the area of the trapezoid. 11 ft

13 ft

16 ft

Area of a Rhombus

The area of a rhombus is half the product of the lengths of its diagonals.

A =

Example: Find the area if the diagonals are: 6 in and 8 in

Area of a Kite

The area of a kite is half the product of the lengths of its diagonals.

A =

Example 1: Kite with diagonals 9 cm & 8 cm

Example 2--Kite

Find the area of the kite. 5”

4”

A = 6”

Formulas

Square: A = bh

Rectangle: A = bh

Parallelogram: A = bh

Trapezoid: A = h

Triangle: A = ½ bh

Rhombus: A =

Kite: A =

Area Addition Postulate

The area of a region is equal to the sum of the areas of its nonoverlapping parts.

Best way to find this area is to find the

area of rectangle + area of triangle

Example—Partitioning Shapes

Find the area of the shape below:

4

9

14 13

16

Find the sum of the areas of the rectangle and the triangle