Question

The adjacent sides of a parallelogram measure 14 centimeters and 20 centimeters, and one angle measures 57 degrees? What is the area of the parallelogram?

Answer 1

start by drawing a diagram, or using the diagram



so there are 2 ways to do this problem.

1. find the perpendicular height of the parallelogram

\[\sin(57) = \frac{h}{14}\]

so

\[h = 14 \times \sin(57)\]

then use the area formula

\[A = base ~~ \times ~~ height\]

Answer 2

|a 2nd method involves using the trig formula for area after drawing a diagonal.

\[A = \frac{1}{2} a \times b \times \sin(C)\]

|dw:1415308882850:dw

where a = 14, b = 20 and angle C = 57

when you have the area of the triangle, just double it for the area of the parallelogram.

hope it helps

Answer 3

how would i find the base since you have to make a right triangle? @campbell_st

Answer 4

the base remains 20