Question

what is the area of a parallelogram with a 45 degree angle and sides of length 6 cm and 7cm.

Answer 1

Area of a parallelogram = absinC
where C=included angle, a and b are the lengths of the included sides.

Answer 2

not to scale

triangle sum of inner angles = 180 degrees

90 perpendicular
half

45 degrees
45 degrees
90 (perpendicular)
-----------
180

2 triangles




form
rectangle
have properties of parallelogram

Area of parallelogram (rectangle)
area Rectangle
A= lw
sides 6
7
A = ( 6 ) ( 7 )

A = 42

Area of the Parallelogram
(in this coincidence a rectangle)
42 cm ^2

Answer 3

This diagram shows why we need to multiply by sin(45) to the product of the two sides.