Cambridge Maths Academy

수학 모음 (Maths collection) 전체보기 To find the surface area of a circular cone, we need to consider the area of the circular sector and the area of the circle. The area of the circular sector: We find the angle $\theta$ by considering the arc length, i.e. $$ \begin{align} L=2\pi\ell\times\frac{\theta}{360}&=2\pi r \\ \Rightarrow\quad \ell\times\frac{\theta}{360}&=r \end{align} $$ The area is then $$ ..

수학 모음 (Maths collection) 전체보기 1. Area of a regular octagon Question. Find the area of a regular octagon with side length $a$. (4-9 Higher GCSE by Michael White, Ch13 Geometry 4, p.426 Q19.) We consider the area of the triangle with an angle $\theta$ subtended at the centre. $$ \begin{align} \theta=\frac{360}{8}=45^\circ \end{align} $$ The height $h$ of the triangle is given by $$ \begin{align} \..

수학 모음 (Maths collection) 전체보기 Heron's formula calculates the area of a triangle. Here, we will look at two different formulae describing the area of a triangle and then derive the third version, Heron's formula. $A=\frac12ah$ $A=\frac12ab\sin C$ Heron's formula: $A=\sqrt{s(s-a)(s-b)(s-c)}\,$ where $s=\frac{a+b+c}{2}$. s can be thought of as half the perimeter of the triangle. As we will see, the..