Find the area of the quadrilateral

How to find the area of a quadrilateral

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[lasalleman]

(1) Set up a right triangle using BC and DC. Go Pythagorean, get a hypotenuse of 26. Thus: area of right triangle BDC: 120. (2) Set up new acute scalene triangle, BAD. Use Heron's formula. Area: 179.6. Total area of quadrilateral: 299.6. -- Short and sweet.

[is]

Same approach as yours and I did it in my mind in 2 mins!

[WahranRai]

Principle of an easy solution : Divide the quadrilateral into 2 triangles, combine Pythagoras and Heron formula`!

[michaeldoerr]

The area is 4[30+12sqrt(14)]. I am glad that I needed a more than sufficient explanation for this type of problem. I am going to use this as practice on similar problems on PreMath and more!!! I hope that this shows that I am serious about being a mathematician!!!

[murdock]

φ = 30°; ∎ABCD → AB = 20; BC = 24; CD = 10; AD = 18; DCB = 3φ → BD = 26
BAD = ϑ → 26^2 = 18^2 + 20^2 - 2(18)(20)cos⁡(ϑ) → cos⁡(ϑ) = 1/15 →
sin⁡(ϑ) = √(1 - cos^2(ϑ)) = 4√14/15 → area ∎ABCD = 120 + (1/2)sin⁡(ϑ)18(20) = 24(5 + 2√14)

[MrPaulc]

Right triangle CBD has an area of 120un^2 and BD is 26 due to sqrt(676).
Area ABD can be found by Heron's formula, though I suspect it's simpler than that.
sqrt((32)(6)(12)(14))
sqrt(32, 256) = 179.6 (rounded)
Add the two answers for 299.6un^2 (rounded).
I have now looked and see you did it the same way. I take on board the way you reduced the square roots in order to make it easier, so thank you for that. Maybe it would be a good idea to call the formula by name - Heron's Formula. That way a student will be able to reference it more easily.

[oscarcastaneda]

Hmm...

Construct the Hypotenuse and determine the length to be 26.

From this, find the area of the 20, 18, 26 triangle via Heron's formula and add the area of the right triangle.

I commented before seeing the solution and I'm glad that we think ALIKE : )

[plamenpenchev]

Heron formula for quadrilateral:
p = (10 + 18 + 20 + 24)/2 = 36
A = sqrt((36 - 10)×(36 - 18)×(36 - 20)×(36 - 24))

[chekyjamoles]

I just discovered different way how to solve area of any triangle with just 3 given line

[gregc.mariano]

Thanks for the lesson but I suppose the explanation is a bit boring. The Heron’s formula should have been mentioned for the sake of those who don’t know. It should have been simpler if you just extract the square root of the product of 32*14*12*6 using the calculator which is 179.6.
As we are taking the area of the figure we should not forget to write square units to the answer if the unit (i.e., ft, inch, m, etc) is not specified. The answer should be 299.6 square units.

[NTA_]

Sir a humble request please raise the level it is class 7 question