ABCDEF is a regular hexagon of side 12 cm. What is the area of triangle BDE?

Question

PLS. explain

Answer 1

124.707 = 72srt3 = area

Beth G was right until she said a 30-60-90 deg triangle has sides of the ratio 3-4-5... its sides actually have a ratio of 1-2-srt3
In this case 12-24-12srt3

I dont know how Shahu got 216?

Area = 124.707 cm^2 = 72srt3

Answer 2

sounds like you have some math homework here. okay, here it is...

area is 96.

1. hexagon has total of 720 degrees. Divide by 6. each angle is 120

2. your triangle BDE has a right angle (90) at D. E is a 120 degree angle of hexagon, but cut in 2. So in the BDE trtiangle, E is 60 degrees. Triangles have 180 degrees. So, B is 30 degrees

3. What you have is a 30-60-90 triangle with one side equaling 12. RULE: on a 30-60-90 triangle, the proportions of the sides are 3-4-5. So, if the shortest side is 12, thats the 3 side. 3x4=12
side BD is the next longer side, so thats the 4 side. 4x4=16. BE is the longest, the 5 side. 5x4=20.

solution: area = bh/2 12x16/2=96.

Best wishes!

Answer 3

this will give us a right angled triangle (with the right angle at D) so we can use that information in finding the overall area of the triangle where area = 1/2 (base x height)

height will be DB and base will be DE= 12 cm

the length of EB = 24 cm (2 hexagon side lengths)

by using pythagorus we find that

EB^2 = DE^2 + BD^2

which leads to BD^2 = 24^2 - 12^2
= 12^2 (4-1)
= 192

which by square rooting both sides

BD = 12 x rt3

so to find the area of the triangle

1/2 x 12 rt3 x 12 = 72rt3 cm^2

Answer 4

Since ABCDEF is a regular hexagon, one can deduce that all sides is equal to 12cm...

**i am not able to draw the diagram here but i hope you can try to visualize it..**

in order to find the area of Triangle BDE, we need to determine the length of BD first.. to do so, we can make use of sine rule with the aid of Triangle BCD...

Angle BCD = [(n-2) * 180°]/n [where n=number of side]
= [(6-2) * 180°]/6
= 720°/6
= 120°

knowing that BC=CD=12cm, Triangle BCD is indeed an isosceles triangle..

Thus, Angle BDC = (180°-120°)/2
= 30°

Now, you can apply the sine rule to determine length of BD...

(sine 120°)/BD = (sine 30°)/BC

(sine 120°)/BD = (sine 30°)/12

0.866/BD = 0.5/12

BD = 0.866 / 0.04166
= 20.78 (rounded off)

Now you can find the area of Triangle BDE by using the formulae
(1/2) * base * perpendicular height

Area of triangle BDE = 1/2 * 12 * 20.78
= 124.7 cm^2.....(rounded off)

**hope you can understand my explanation**

cheers... (",)

Answer 5

216 sq.cm