Question

geometry and area: find the area of a parallelogram if the two sides measure 24.1 inches and 31.4 inches and the shorter diagonal is 32.4 inches.

Answer 1

so the diagram looks like

Answer 2

oops missed a side

Answer 3

so have you done the law of cosines and area of a triangle using trig..?

Answer 4

yes

Answer 5

ok... so this is what I would do

find the size of the angle x

using the law of cosines... to find x

then use the area of a triangle

\[A = \frac{1}{2} \times 24.1 \times 31.4 \times \sin(x)\]

which gives the area of the lower triangle and double it to get the area of the parallelogram

does that make sense..?

Answer 6

ok

Answer 7

but I don't have any angles to use the law of cosines its 3 sides right

Answer 8

yes, for an angle and if you made cos(x) the subject of the formula you would get

\[\cos(x) = \frac{24.1^2 + 31.4^2 - 32.4^2}{2 \times 24.1\times 31.4}\]

Answer 9

ok I see

Answer 10

the right side of the equation gives a value less that 1...

so

\[x = \cos^{-1}(answer)\]

Answer 11

I did 1/2(24.1*31.4*70) = 26485.9

Answer 12

I think you forgot its sin(70)

I think the angle is correct...

\[Area = \frac{1}{2} \times 24.1 \times 31.4 \times \sin(70)\]

Answer 13

then double that area for the area of the parallelogram

Answer 14

355*2

Answer 15

yes... just be careful with rounding 2 early... Id say 711 inches^2

Answer 16

thank u so much

Answer 17

glad to help...