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CoRRupt3d

Guest

Need Help with Quadrilateral Problem

The bases of trapezoid ABCD are AB and CD. Let M be the midpoint of AD. If the areas of triangles ABM and CDM are 5 and 17, respectively, then find the area of trapezoid $ABCD$.

The bases of trapezoid ABCD are AB and CD. Let P be the intersection of diagonals AC and BD. If the areas of triangles ABP and CDP are 8 and 18, respectively, then find the area of trapezoid ABCD.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need Help with Quadrilateral Problem

For Q1: Since M is the midpoint of AD, we can draw the median for trapezoid ABCD that meets CD at N. We can also draw a height from A to DC, let that be Y and the intersection of MN and AY be X. Let AB=a and CD=b

EDIT: Now with Latex!

Last edited by evene (2015-12-05 03:45:48)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,136

Re: Need Help with Quadrilateral Problem

hi CoRRupt3d,

Welcome to the forum.

You can also use evene's method for the second part but the algebra is more complicated.

Let a and b be the lengths of the parallels; h1 is the height of triangle ABP and h2 of CDP

Since triangle ABD has the same base as ABP, its area is given by

I'll leave you to get a similar expression for the area of BCD.

Now triangles ABP and CDP are similar so their lengths are in a certain ratio, and their areas are in the same ratio squared.

So you can get the value of h1/h2 and also h2/h1.

So you can calculate the area ABCD from ABD + CDB.

Hint:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need Help with Quadrilateral Problem

I have a question: Does this forum use Asymptote too? Asymptote is a thing where you can draw manual diagrams! It's amazing!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need Help with Quadrilateral Problem

You can try geogebra.

http://www.geogebra.org/

Or try it online first.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Need Help with Quadrilateral Problem

ok thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need Help with Quadrilateral Problem

Hope you enjoy it, it is very powerful.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.