Will you help me with this geometry question, please?

Question

Will you help me with this geometry question, please?
Thank you a bunch.
And show/explain how to get the result?

What is the area of a 13 by 14 by 15 triangle?

Thanks a bunch. <3

Answer 1

The semi=perimeter of the triangle
=(13+14+15)/2=21 units
Therefore the area of the triangle
=sqrt{21*(21-13)*(21-14)*
(21-15)
=sqrt(21*8*7*6)
=sqrt7056
=84 sq.units

Answer 2

Check out the source. The fourth method seems pretty easy and I have included it here. The method is proved on the web page.

4. Area = sqrt(s*(s-a)*(s-b)*(s-c))
where s=(a+b+c)/2 is the semi-perimeter.

So s = (13 + 14 + 15)/2 = 21
Area = SQRT(21*(21 - 13)*(21 - 14)*(21 - 15))
Area = SQRT(21*8*7*6) = SQRT(7056)
Area = 84

If you want an easy one to show the method then:

If the triangle has vertex C at the top, A to the left, B to the right and base along the bottom. Using "a", "b" and "c" as the lengths of the sides opposite angles A, B and C.

c = length of base = 15 and a=13 and b=14 (a and b can be interchanged if you like but if so the calculations below must be changed)
h = height of the triangle

Area = c*h/2 .... standard formula for the area of a triangle (one half the base times the height)

You know "c" so you just need "h".

h = b*sin(A) ..... see description of triangle above

Use the law of cosines to get the angle A.
a^2 = b^2 + c^2 - 2bc*cos(A)
cos(A) = (b^2 + c^2 -a^2)/(2bc)
cos(A) = (14^2 + 15^2 - 13^2)/(2*15*14)
cos(A) = (196 + 225 - 169)/390 = 252/420
cos(A) = 6/10 and sin(A) = 8/10 ... right triangle: 6-8-10

Area = c*b*sin(A)/2 = 15*14*(8/10)/2 = 168/2
A = 84 Which agrees with that other way

Answer 3

This will be more difficult without a diagram, but here goes nothing. First, draw a diagram of the triangle, placing the side 15 on the bottom, 13 on the left, and 14 on the right. The formula for area is 1/2 base x height. To obtain the height, draw a line dividing the triangle into two right triangles. Next, label the left division of the base x and the right division 15-x. The pythagorean theorem tells us that c squared (denoted c^2) = a^2 + b^2. We may thus set up the equation 13^2 - x^2 = 14^2 - (15-x)^2 (this is possible because both are equal to the same side, the height). Expanding, we get 169 - x^2 = 196 - 225 + 30x - x^2. Solving yields x = 6.6. Plugging this into the area equation produces A = 1/2 (15 x 6.6) = 49.5. Any questions, then just contact me.

Answer 4

usually to find the area of the triangle, we have the formula as
1/2 * base * height
but here, since the sides are given, the formula is
sqare root [s(s-a)(s-b)(s-c)], where s=(a+b+c)/2
here a=13, b=14,c=15
s=(13+14+15)/2=21
Area of the triangle=sqrt[21*(21-13)(21-14)(21-15)
=sqrt[21*8*7*6]
=sqrt(7056)
=84
n.b: you have not mentioned the unit of measure
if the sides are measured in cms, then the answer is 84sqcm

Answer 5

On the web:
http://en.wikipedia.org/wiki/Triangle

There you'll find: (a=13, b=14, c=15 your case)
The area S of a triangle can be found using Heron's formula
Let a, b, c be the sides of the triangle.
The shape of the triangle is determined by the lengths of the sides alone. Therefore the area S also can be derived from the lengths of the sides. By Heron's formula:

S = \sqrt{s(s-a)(s-b)(s-c)}

where s = ½ (a + b + c) is the semiperimeter, or half of the triangle's perimeter.

Answer 6

use the 14 side as your base, then draw a line straight down from the top vertex perpendicular (makes 90 degrees) to that base. So you will have each side of the base be 7 and your hypotenuse as 13 then
13^2=x^2+7^2
169=x^2+49
x^2=120
x=10.9
area = .5*base*height
.5*14*10.9=76.3

Answer 7

1/2 Base x Height

Answer 8

somewhat, the only component that i will discover in uncomplicated with sacred geometry and alchemy is they the two manage forms of spirituality. Sacred geometry deals with using geometric varieties and shapes in the layout and shape of churches, temples, mosques or everywhere of non secular amassing. those specific shapes advise specific issues, finding on the religion or concept gadget. as an occasion, the pentagram in Christianity refers back to the 5 senses. In Catholicism, it could now and back talk with the devil, or the Evil One. Alchemy deals with the technique of turning metals into gold, utilising chemical ingredients and technology. regardless of the undeniable fact that, Alchemy is likewise a concept find the applicable understanding via chemistry. consequently, alchemy is a spirituality all its very own. All in all, the only component that i will see in uncomplicated between the two is they the two manage a kind, or types, of spirituality.

Answer 9

math is for nerds.

...that's why they call them "math nerds".