Question

Find the area of an equilateral triangle with side length 4.6 cm. Round your answer to 1 DP.

Answer 1

10.58
The areas of a triangle is b*h / 2
4.6*4.6 = 21.16
21.16/2 = 10.58
This is because it is an equilateral triangle so all side lengths are the same

Answer 2

Answer:

A = 9.2 cm²

Step-by-step explanation:

A = 1/2 bh, you know the base = 4.6 and you need to find the height of the triangle.

Drawn the attitude of the equilateral triangle to the base and use a² + b² = c²

c = side of the triangle = 4.6 , b = 1/2 0f 4.6 = 2.3 . the attitude to the base ÷ the base in half.

a² + (2.3)² = (4.6)²

a² + 5.29 = 21.16

a² = 21.16 - 5.29

a² = 15.87

$a = \sqrt{15.87}$  

Now we know the height of the triangle = $\sqrt{15.87}$ , the base = 4.6

A = 1/2bh

A = 1/2 (4.6)($\sqrt{15.87}$ )

A  = 9.1625

A = 9.2 cm²    or the A of any equilateral triangle = $\frac{\sqrt{3} }{4} s^2$

                                              A = $\frac{\sqrt{3} }{4} (4.6)^2$

                                              A = 9.1625

                                              A = 9.2