can you please help me find the answer

Question

ind the area of the figure.  Round to the nearest hundreth.

A=  in²

Answer 1

If it is given the triangle is equilateral and point is centroid of triangle,

then altitude of triangle is 8.5+17=25.5,,,,property of centroid

base is 51/√3,,,Pythagorean theorem

area=(1/2)(25.5)(51/√3)=375.42 sq units

Answer 2

If you connect 3 straight lines from the center of the triangle to each vertex, you will now have 3 triangles inside the original triangle. The areas of these 3 triangles are the same as that of the original triangle. The angle by the center of the original triangle is 360/3 = 120 degrees.

Then, construct perpendicular bisectors of each original side. You now have 6 congruent triangles which, when combined, have the same area as the original triangle.

The angle by the center of the original triangle is 120/3 = 60 degrees.

The area of each of these 6 new triangles is (1/2)*8.5*8.5*tan(60 degrees), and 6 times this value results in 375.42 square inches, rounded to 2 decimal places.