DEVELOPING FORMULAS FOR TRIANGLES AND QUADRILATERALS Geometry CP1 (Holt 10-1)K. Santos.

DEVELOPING FORMULAS FOR TRIANGLES AND QUADRILATERALS

Geometry CP1 (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

A = 9(3)

A = 27

Example

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

Need to find height

A = bh

12 = 4h

h = 3 ft

P = 2b + 2h

P = 2(6) + 2(3)

P = 18 ft

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”

Then A = (4)(6)

A = (24)

A = 12

Example—finding a side

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

A = for a triangle

24=

48 = 3b

b = 16 cm

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 in

36 in

A = h

A = 18

A = 18

A = 28(18)

A = 504

Example 2--Trapezoid

Find the area of the trapezoid. 11 ft

13 ft

16 ft

A = h find the missing height Find the hypotenuse

Use Pythagorean theorem

when solved you get …… h = 12 ft

A = 12

A =( ) 12

A = 27(6)

A = 162

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

A =

A =

A =

A = 24

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

A =

A =

A =

A = 36

Example 2--Kite

Find the area of the kite. 5” 4”

A = 6”

Find diagonalsWatch for right triangles = + so x = 3”

One diagonal is 2(4) = 8 inches Other diagonal = 3 + 6 = 9 inchesA = A = A = 36

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 16Find the sum of the areas of the rectangle and the triangle A = bh A = A = 4(14) A = A = 56 A = 30 total area: 56 + 30 = 86