Would you use this method to find the area of Blue shaded triangle? | Trapezoid

Would you use this method to find the area of Blue shaded triangle? | Trapezoid | Trapezium

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Жыл бұрын

Learn how to find the area of Blue shaded triangle in the Trapezoid. Important Geometry and algebra skills are also explained. Step-by-step tutorial by PreMath.com
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Would you use this method to find the area of Blue shaded triangle? | Trapezoid | Trapezium
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Пікірлер: 85

@walcholjacob4259 Жыл бұрын

Interesting one☺

@PreMath Жыл бұрын

Glad you think so! Thank you! Cheers! 😀

@juuusturull1250 Жыл бұрын

Great video! You didn't even need to find the area of the trapezoid nor the white triangle. If the base of the blue triangle is 25 and height is 24, you can find the area of the blue triangle easily.

@PreMath Жыл бұрын

You are right! Thank you! Cheers! 😀

@xof-woodworkinghobbyist Жыл бұрын

I did the same way.

@bb55555555 9 ай бұрын

My thought exactly. As soon as you got the 25 for the base you already had the height of the triangle.

@burlfromlondon Жыл бұрын

After you know the value of AB then you can directly calculate the area just using half base times height

@PreMath Жыл бұрын

True! Thank you! Cheers! 😀

@soli9mana-soli4953 Жыл бұрын

And you can call not EA but AB = X, then X² = 24² + (32 - X)² it's a little faster

@pwmiles56 Жыл бұрын

By Pythagoras DB is 40. Drop a perpendicular from A to P on DB. As ABD is isosceles P is the midpoint of DB, DP=PB=20. Triangle APB is similar to triangle BCD (as angle ABP is complementary to CBD and PAB is complementary to that). So AP = (24/32)x20 = 15 Area of ABD = 40(15/2) = 300

@PreMath Жыл бұрын

. Thank you! Cheers! 😀

@dalesmith7250 Жыл бұрын

This is exactly what I did

@NYlivinginTN Жыл бұрын

Same here

@Mattdemon08 Жыл бұрын

Lovely! 👍🏾

@misterenter-iz7rz Жыл бұрын

Clearly BD=40, it remains to find the height h of the triangle, in view of similar triangles, h/20=24/32=3/4, thus h=15, therefore the answer is 40x15/2=300.😃

@PreMath Жыл бұрын

. Thank you! Cheers! 😀

@himo3485 Жыл бұрын

AB=AD=x (32-x)^2+24^2=x^2 1024-64x+x^2+576=x^2 64x=1600 x=25 area of the Blue Triangle : 25＊24/2=300

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@anthonycheng1765 Жыл бұрын

angle BDC = atan(3/4). angle ABD = atan(3/4) (alt angles, DC // AB), AB = AD (given), angle ADB = angle ABD (base angles isos. triangles). Draw AE perpendicular to DB with BE = ED. AE = sqrt(24^2 + 30^2) = 40 (Pyth. Thm) BE = ED = 20. AE = 20*tan(atan(3/4)). Area = 1/2*AE*BD = 1/2*40*20*tan(atan(3/4)) = 300

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@gassawi Жыл бұрын

Where 30^2 is coming?

@anthonycheng1765 Жыл бұрын

@@gassawi sorry it is 32^2

@Abby-hi4sf Жыл бұрын

I love outside the box, because it expands our vision to any problem! Thank you!

@ybodoN Жыл бұрын

Draw a perpendicular from A to E on DB. As DC ∥ AB ⇒ ∠CDB ≅ ∠DBA ⇒ ◺BCD ~ ◺BEA. DB = √(24² + 32²) = 40 ⇒ EB = 20. AB = 40 ⋅ 20 / 32 = 25. Area △ABD = ½ 25 ⋅ 24 = 300 u².

@williamwingo4740 Жыл бұрын

A slightly different method: Let x = AB = AD, and draw triangle ADE as you did. Then by Pythagoras, x^2 = 24^2 + (32 - x)^2; multiply out (32 - x)^2: x^2 = 24^2 + 32^2 - 64 x + x^2; subtract out x^2: 0 = 24^2 + 32^2 - 64x; rearrange: 64x = 24^2 + 32^2; solve for x: x = (24^2 + 32^2)/64 = (576 + 1024)/64 = 1600/64 = 200/8 = 25. And the area of the blue triangle is (1/2)(24)(25) = (12)(25) = 300. It might also be worth noting that triangle ADE is integer Pythagorean, 7-24-25. Cheers. 🤠

@alster724 Жыл бұрын

Interesting and easy at the same time

@sumanmukherjee100 Жыл бұрын

It was a pretty good question sir.. I first drew a perpendicular from point A to line DC , which is AP then I took AB =x then i got DP=32-x as AP is perpendicular it was 24as well the by Pythagorean theorem I got AD is 25 . And the the area of the traingle is half times base times hight and the I got area =25×24/2 = 300units .. thank you sir love from India..

@PreMath Жыл бұрын

So nice of you dear Thank you! Cheers! 😀

@allanflippin2453 Жыл бұрын

Yes, I used this approach as well. It saves a couple steps. We no longer need the area of the trapezoid, just calculate the triangle area directly.

@sumanmukherjee100 Жыл бұрын

@@allanflippin2453 yeah , you are correct..I think this is one of the easiest approach..

@Mattdemon08 Жыл бұрын

Good question. It was a good brain workout for me. I noted from your video and the comments how i could have skipped some of my steps. Thank you.

@PreMath Жыл бұрын

Great job! So nice of you. Thank you! Cheers! 😀

@harikatragadda Жыл бұрын

Draw a perpendicular from A to DB at E. AE divides triangle ABD into two right triangles with base 20. Triangle AEB is Similar to Triangle DCB, AE = BE*CB/DC= 15 Blue area = 2*½*AE*BE = 300

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@anahimaceda7070 Жыл бұрын

Excellent!!! Thanks!

@PreMath Жыл бұрын

Glad you liked it!

@misterenter-iz7rz Жыл бұрын

More generally, let BC=a, CD=b, then BD=sqrt(a^2+b^2), let AE=h be the height of the triangle, so 2h/sqrt(a^2+b^2)=a/b, thus h=a sqrt(a^2+b^2)/(2b), and then the area is sqrt(a^2+b^2)a sqrt(a^2+b^2)/(4b)=(a^2+b^2)a/(4b). It is 300, as a=24, b=32.

@ybodoN Жыл бұрын

Otherwise, DB = √(a² + b²) ⇒ EB = ½ √(a² + b²) ⇒ AB = ½ (a² + b²) / b ⇒ area △ABD = ¼ (a² + b²) a/b which, of course, is just an alternate form of the same general formula.

@TimBoulette Жыл бұрын

Extend line AB to the left, and drop an auxiliary line from point D to point P such that it completes rectangle BCDP. Line DP is equal to line CD, which is 24. Let x = line PA. Then, AB = 32-x, as does line AD. Pythagorean theorem: x^2 + 24^2 = (32-x)^2. Solve for x and you get x = 7. Therefore, AB= 25. Area of ABD = (1/2)*24*25 = 300.

@mohanramachandran4550 Жыл бұрын

at. 6 : 38 we find AB = 25 Then area of the blue triangle is ½bh = ½ *25*24 = 300 square units

@jhouck1969 11 ай бұрын

A simpler solution: Triangle BCD is a 3-4-5 triangle, so length BD = 40. Because sides AB and CD are parallel, angle CDB = angle DBA. Bisect angle DAB creating a perpendicular bisector of side BD, making two identical 3-4-5 triangles with sides 15-20-25. This means the height of triangle ABD is 15 and the base is 40. Thus the area of triangle ABD is (1/2)(15)(40) = 300.

@KAvi_YA666 Жыл бұрын

Thanks for video.Good luck sir!!!!!!!!!

@PreMath Жыл бұрын

Thank you too

@yamunaravi7132 Жыл бұрын

Very good 👍

@raya.pawley3563 11 ай бұрын

Thank you!

@PreMath 11 ай бұрын

You're welcome!

@juanalfaro7522 7 ай бұрын

It is good to find alternate ways of solving problems, but I would have used the direct way: I find the length AB by finding the angle ABD, which is the complement of angle CBD, then determine the area either as (1) AB x BD x sin (ABD / 2, or determining the H from A to the midpoint of BD and then calculating Area = BD x H /2. BD is easily determined by the 3-4-5 rule as 40 and angle ABD is the complement of 53.13, which is 36.87. So cos (36.87) = 0.6, sin (36.87) = 0.8, AB = 25, and H = 15. Clearly the area is 300.

@engralsaffar 10 ай бұрын

In 3,4,5 right triangle DB=40 We can connect A to point M in the middle of DB, to get a 2 right triangles Triangles DBC and AMB are similar triangles 24/32=AM/20 AM=15 A=15*20=300 square units

@quigonkenny 5 ай бұрын

Let AB = DA = x. Let E be a point on CD such that EA is parallel to BC. By observation, ED = 32-x. Since the point of this video seems to be trapezoids, by the title, we'll determine the area by finding the difference in area between the trapezoid ABCD and triangle ∆BCD, though it would be simpler just to determine the area of ∆DAB directly once we have x. Triangle ∆AED: a² + b² = c² (32-x)² + 24² = x² 1024 - 64x + x² + 576 = x² 64x = 1600 x = 25 Triangle ∆BCD: A = bh/2 = 32(24)/2 = 384 Trapezoid ABCD: A = h(a+b)/2 = 24(25+32)/2 A = 12(57) = 684 Triangle ∆ABD: A = 684 - 384 = 300 Double check: A = bh/2 = 25(24)/2 = 600/2 = 300

@bearantarctic5843 Жыл бұрын

Or alternatively: Find angle CBD using trigonometry Find all of the angles in the blue triangles Find that DB is 40 units long using the Pythagorean theorem Find that AB is 25 units long using the Law of Cosines Calculate the area of the triangle using Heron's formula A little bit of trig didn't hurt anyone

@bobbyheffley4955 11 ай бұрын

Let the legs of the isosceles triangle be 25 units in length and the longer side be 40 units in length. 25+25+40=90 units. Half of that is 45. 45-25=20 45-40=5 By Heron's formula, the area is sqrt [45(20)(20)(5)]=sqrt (90,000)=300

@bahijsarhan8002 Жыл бұрын

Bd=40 حسب فيثاغورث نرسم الارتفاعam علىbd فهو متوسط الزاويةbdc=abd تبادل داخلي نحسب cosالزاويتان 20/x=32/40 نجدx=25 S=25×24/2=300

@MrPaulc222 9 ай бұрын

i never found AB or AD. Instead, I found the diagonal to be 40 due to 8(3) + 8(4) = 8(5). Then

@brianrsnes7875 Жыл бұрын

I too made the DEA triangle and found x to be 7. But I subtracted triangle DEA from triangle DEB. Thus half time heigt on both is 12. (12*32)-(12*7)=12*25=300

@giuseppemalaguti435 Жыл бұрын

A(blue) =bh/2=20/cos(90-arcsin32/40)*24/2=25*24/2=300

@chanpangchin9744 7 ай бұрын

Mentally guessed 7,24,25. Area of blue region=1/2 x 25x24=300

@cleiberrocha1449 6 ай бұрын

Once we find the value of AB = 25, just calculate the area of the triangle ABD = (1/2) 25×24 =25 ×12= 300

@sie_khoentjoeng4886 11 ай бұрын

Alternative way, we can calculate the blue area after calculate AE, here AE = 7: ABD = EBD - EAD ABD = (32*24)/2- (24*7) /2 ABD = 768/2- 168/2 ABD = 384 - 84 ABD = 300

@vidyadharjoshi5714 Жыл бұрын

DB = 40. Angles ABD & ADB = 36.87 each. Cos 36.87 = 20/AB = 0.8. So AB = 25, So Blue Area = 0.5*24*25 = 300

@MarieAnne. Жыл бұрын

To calculate area of triangle ABD, we need only use the formula Area = 1/2 * base * height where base = AB (which you calculated between 2:45 and 6:43) and height = 24 (given). So once we've found length of AB = 25, we get: Area = 1/2 * 25 * 24 = 300

@bigm383 Жыл бұрын

A little convoluted but worthwhile!🥂👍❤

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@user-lk4ky6ch9s Жыл бұрын

△ABD=x AB=x/12=AD (32-AB)^2+24^2=(x/12)^2 x=300

@santiagoarosam430 Жыл бұрын

24²+32²=DB² → DB=40 → Si “M” es el punto medio de DB→DM=MB=40/2=20 → El punto A equidista de B y D → El punto A pertenece a la mediatriz de DB → La razón de semejanza “s” entre los triángulos rectángulos AMB y BCD es s=20/32=5/8 → AM=24*5/8 =15 → Área azul =20*15=300 Gracias y saludos.

@mohamadtaufik5770 Жыл бұрын

DB^2=DC^2+CB^2 DB^2=32^2+24^2 DB=40 tan BDC=24/32=3/4 24^2+a^2=b^2 576+a^2=b^2 b=V576+a^2 h^2+20^2=576+a^2 h^2-a^2=176 a+b=32 --> b=32-a 576+a^2=(32-a)^2 576+a^2=1024-64a+a^2 64a=1024-576=448 a=7 --> h^2=176+7^2=225 h=15 Area of blue triangle=0.5*40*15=300 square units

@wackojacko3962 Жыл бұрын

👍

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@BilalSozkesen-dr4im 9 ай бұрын

at the end why are u calculate area of abcd just do that height of abd=24 ab=25 area of abd=25*24/2 =300

@ybodoN Жыл бұрын

Let's play with trigonometry! But first we need to divide the isosceles triangle ABD into two congruent right triangles one side of which is half of DB🧐 Since DC ∥ AB ⇒ ∠CDB ≅ ∠DBA (alternate angles). Let's call this angle θ. Since tan θ = 24/32 = ¾ ⇒ sin θ = ⅗ ⇒ cos θ = ⅘ (trigonometric identities). Then DB = 32 / cos θ = 32 / (⅘) = 40 and AB = ½ DB / cos θ = 20 / (⅘) = 25. So, the area of the blue △ABD is ½ 40 ⋅ 25 ⋅ sin θ = ½ 40 ⋅ 25 ⋅ ⅗ = 300 u².

@user-eo2ed7lr2n Жыл бұрын

We don't need calculate trapezoid's area. If we know AB and AD - we can find triangle's area. AB is a base, BC is a height. AB*BC/2 is a triangle's area

@theoyanto Жыл бұрын

Yeah nice, I did it the other way though, 345's everywhere 🙂

@PreMath Жыл бұрын

Nice job!

@theoyanto Жыл бұрын

@@PreMath cheers 🤓

@AmirgabYT2185 5 ай бұрын

S=300

@acnmes 10 ай бұрын

Pourquoi calculer l’aire du trapèze ? Une fois la base obtenu, la formule de l’aire d’un triangle suffit !

@broytingaravsol Жыл бұрын

easy

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@cefffun 11 ай бұрын

300

@prossvay8744 7 ай бұрын

A=300 square units

@danieldennis9831 Жыл бұрын

300 but I made a mistake first

@jonathansmith7777 Жыл бұрын

That was too long. BCD is 3-4-5 so we know BD = 40 Then find DA from small triangle then 1/2 b*h

@marioalb9726 Жыл бұрын

Taking the white right triangle: c²=a²+b² c²=32²+24² c= 40 cm tan α = 32/24 α = 53,13° β = 90° - α β = 36.87° Taking half blue triangle, which is a right triangle: tan β = h / (c/2) h = c/2. tan β h = 40/2 . tan 36,87° h = 20 . 0,75 h = 15 cm Area of blue triangle: A = c. h / 2 = A = 40 . 15 / 2 A = 300 cm² ( Solved √ )