Question

Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.

Answer 1

In the above triangle, the measurement of the side DC is 5 cm. In the triangle ADC , the side AC is called hypotenuse side whose length is 10 cm.

So we can say $A{C}^2=A{D}^2+D{C}^2{10}^2=A{D}^2+5^{2}100=A{D}^2+25100-25=A{D}^{2}A{D}^2=75AD=\sqrt{75}AD=5\sqrt{3}$

Now we can apply the formula to find the area of triangle = $\frac{1}{2}\times base\times height$

Here base is 10 cm and height is $5\sqrt{3}$ cm

Area of the given triangle = $\frac{1}{2}\times 10\times 5\sqrt{3}=5\times 5\sqrt{3}=25\sqrt{3}c{m}^2$