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Two sides of a parallelogram are 24 feet and 30 feet. The measure of the angle between these sides is 57 degrees. What is the area of the parallelogram to the nearest square foot?

1 Answer

Jan 17, 2016

Area $= 604$ $= 604$ sq. ft.

Explanation:

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$sin (57^{\circ}) = \frac{h}{24 ft}$ $sin(57^@) = h/(24 "ft"$

$\Rightarrow h = 24 ft \times sin (57^{\circ}) = 24 ft \times 0.83867 = 20.128 ft$ $rArr h= 24" ft"xxsin(57^@) = 24" ft" xx 0.83867 = 20.128" ft"$

$A r e a = b a s e \times h e i g h t$ $Area = base xx height$

$XXX = 30 ft \times 20.128 ft = 603.84$ $color(white)("XXX")=30" ft" xx 20.128" ft" = 603.84$ sq. ft.

To nearest square foot
$XXX A r e a = 604$ $color(white)("XXX")Area = 604$ sq. ft.

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