AB = 80 m, BC = 60 m
DF = 50 m, GE = 50 m
HE = 100 m
The area of the whole figure is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7400 m2
The whole figure is made of two triangles sharing the side AC: the right triangle ABC (blue) and the triangle ACE (green), whose height is EH, since EH is perpendicular to AC. AC is not given, so it is found from the right triangle ABC.
Triangle ABC (right angle at B):
\(AC^2=AB^2+BC^2=80^2+60^2=6400+3600=10000\), so \(AC=100\) m
Area \(=\frac{1}{2}\times AB\times BC=\frac{1}{2}\times80\times60=2400\) m2
Triangle ACE (base AC, height EH):
Area \(=\frac{1}{2}\times AC\times EH=\frac{1}{2}\times100\times100=5000\) m2
Whole figure: \(2400+5000=7400\) m2