Question

Question 66

Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area of each sail of the sailboats to the nearest tenth.

Answer 1

In the sailboat (i),
Area of triangle $=\frac{1}{2}\times Base\times Height$
In $\Delta ABC$, AC = Base = 22 + 20 = 42 m
BD = Height = 22.3 m

$\therefore$ Area of $\Delta ABC=\frac{1}{2}\times 42\times 22.3=\frac{936.6}{2}=468.3m^2$
In another triangular part,

In $\Delta ACE,EF=Height=16.8m$
AC = Base = 22 + 20 = 42 m
$\therefore$ Area of $\Delta ACE=\frac{1}{2}\times 42\times 16.8=\frac{705.6}{2}=352.8$

Area ABCE = 468.3 + 352.8 = 821.1 m^2
In sailboat (ii),.
Area of a triangle $=\frac{1}{2}\times Base\times Height$
In $\Delta ABC,\angle B={90}^{\circ }$, base (BC) = 10.9 m and height (AB) = 19.5 m
Area of $\Delta ABC=\frac{1}{2}\times 10.9\times 19.5=\frac{212.55}{2}=106.275m^2$
In another triangular part,

Area of $\Delta DEF=\frac{1}{2}\times DF\times EH$
$=\frac{1}{2}\times 23.9\times 8.6=\frac{205.54}{2}=102.77m^2$
Area of sailboat (ii) $=106.275+102.77=209.045m^2$
In sailboat (iii),
Area of triangle $=\frac{1}{2}\times Base\times Height$
In $\Delta ABC$, AB = 8.9 m and BC = 3m

Area of $\Delta ABC=\frac{1}{2}\times BC\times AB$
$=\frac{1}{2}\times 8.9\times 3=\frac{26.7}{2}=13.35m^2$
In another triangular part,

Area of $\Delta DEF=\frac{1}{2}\times DF\times EG$
$=\frac{1}{2}\times 25\times 12.4=155m^2$
In another triangular part,

Area of $\Delta DEH=\frac{1}{2}\times DE\times EH$
$=\frac{1}{2}\times 9.6\times 16.8=80.64m^2$
$\therefore$ Area of sailboat (iii) = 155+ 80.64
$=235.64m^2$