Question Number 66849 by John Kaloki Musau last updated on 20/Aug/19
Commented by John Kaloki Musau last updated on 20/Aug/19
A girl wanted to make a regular octagon of side 14cm. She made it from a square piece of a card of size ycm by cutting off four isosceles triangles whose equal sides were xcm each, as shown in the figure above. (a) Write down an expression for the area of the octagon in terms of x and y. (b) Find the value of x. (c) Find the area of the octagon.
Commented by John Kaloki Musau last updated on 20/Aug/19
$$\boldsymbol{{The}}\:\boldsymbol{{answers}}\:\boldsymbol{{are}}: \\ $$$$\left(\boldsymbol{{a}}\right)\:\left(\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} \right)\boldsymbol{{cm}}^{\mathrm{2}} \\ $$$$\left(\boldsymbol{{b}}\right)\:\boldsymbol{{x}}=\sqrt{\mathrm{98}}\:\boldsymbol{{or}}\:\mathrm{7}\sqrt{\mathrm{2}}\:\boldsymbol{{or}}\:\mathrm{9}.\mathrm{899}\boldsymbol{{cm}} \\ $$$$\left(\boldsymbol{{c}}\right)\:\mathrm{946}.\mathrm{3}\boldsymbol{{cm}}^{\mathrm{2}} \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{show}}\:\boldsymbol{{me}}\:\boldsymbol{{how}}\:\boldsymbol{{they}}\:\boldsymbol{{are}} \\ $$$$\boldsymbol{{calculated}} \\ $$