Question #d8f28

3 Answers
Oct 7, 2017

Area, A = 16 root\ 3

Explanation:

We can apply Heron's formula to find area of the given triangle.

Area of triangle A = root \ ((s(s-a)(s-b)(s-c))

where, a,b and c are sides of the triangle and s is the semiperimeter of the triangle and is given as:

s= (a+b+c)/ 2

In equilateral triangle a=b=c

Here a is given as 8.

So semiperimeter s = (a+a+a)/2 =(3a)/2 = (3\timescancel8^4)/cancel2^1 = 12

Area, A = root \ ((s(s-a)(s-b)(s-c))

A = root \ ((3a)/2((3a)/2-a)((3a)/2-a)((3a)/2-a))

A = root\ ((3a)/2((3a-2a)/2)((3a-2a)/2)((3a-2a)/2))

A = root \ ((3a)/2((a)/2)((a)/2)((a)/2))

A= root \ ((3a^4)/2^4 = root \ ((3a^4)/16

A = root \ 3 \times a^2/4

Here a =8

A = root \ 3 \times 8^2/4

A = root \ 3 \times 64/4

A = root \ 3 \times 16 = 16 root\ 3

or
A = root \ ((s(s-a)(s-b)(s-c))

A = root \ ((12(12-8)(12-8)(12-8))

A = root \ ((12(4)(4)(4))

A = root \ ((3\times(4)(4)(4)(4))

A = root \ ((3\times 256))

A = 16 root\ 3

Oct 7, 2017

Let's make it easy.

Explanation:

Let, each side of length 8units be "a".
So, a=8.

Now, Area of a triangle, A=1/2xxhxxb....(1)
where, h is height & b is base.
Here, b=a=8....(2)

Now, by Hypotenuse Principle rarr
h=sqrt(a^2-(b/2)^2).
:.h=sqrt(a^2-(a/2)^2)
...From (2).
:.h=sqrt((3a^2)/4).

So, h=(asqrt(3))/2.

Therefore, from (1) rarr
A=1/2.a.(sqrt(3)a)/2.

:.A=(sqrt(3)a^2)/4.

Now, substituting the respective values rarr
A=(sqrt(3).8^2)/4.
:.A=16sqrt(3).
(Answer).

Hope it Helps!!

Oct 7, 2017

A= 27.71 square units

Explanation:

The simplest and most direct method of finding the area of an equilateral triangle is by using the trig area rule.

All the sides are 60° and all the sides are of length 8 units.

Therefore the requirements of two sides and the included angle are met.

Area = 1/2 a*b*sinC

A= 1/2 *8*8*sin60

A=1/2*8*8*sqrt3/2

A=16sqrt3

A= 27.71 square units