Question 695710
{{{drawing(300,100,-18,18,-1,11,
triangle(-10sqrt(3),0,10sqrt(3),0,0,10),
rectangle(0,0,-1,1),green(line(0,0,0,10)),
locate(0.5,6,h),locate(8.7,6.5,20),locate(-10,6.5,20),
locate(-8.5,2,x),locate(7,2,x),
locate(-14.5,2.8,30^o)
)}}} We can calculate the lengths of legs in the right triangles.
{{{h=20*sin(30^o)=20*(1/2)=highlight(10)}}}cm
{{{x=20*cos(30^o)=20*(sqrt(3)/2)=highlight(10sqrt(3))}}}cm
The area of a triangle is calculated as
{{{area=(1/2)*base*height}}}
For the isosceles triangle, so
{{{base=2x}}} and {{{height=h}}}, so the area (in square centimeters) is
{{{area=(1/2)*(2x)*h=x*h}}}, so the area (in square centimeters) is
{{{area=10*(10sqrt(3))=highlight(100sqrt(3))}}} = approx. 173.2 square cm