It is 0.5 square mm.
The hypotenuse of a triangle with a base of 300 mm and 500 mm height is: 583.1 mm
38.4 sq. mm
It is: 0.5*6*8 = 24 square mm
I am going to assume you mean the by radius of the equilateral triangle, you mean the radius of the circumcircle of the triangle. This is the circle that passes through all 3 vertices of the triangle. This is 8 The apothem is 4 and it is the short vertical line from the center to the midpoint of an edge. Construct a right triangle with the one side being the apothem and the hypotenuse being the radius. The length of the other side ( the missing one for which you are solving) is 1/2 the length of the side of the equilateral triangle. A picture will help you see this. Now area will be this times the altitude of the triangle. Or you can directly use the fact the the area is (square root of 3 )/ 4 x (the length of the side squared. ) So in this case 1/2 the length of the side is square root of 48 or 4(square root 3) Now to find the area we square this entire quantity after we multiply it be 2 since it was half the side and multiply by (Square root of 3)/ 4. So the side length is 2(sqrt 48) or 8(sqrt 3) When you square this you have 192 now to finish just multiply this by (sqrt3)/4 to find area. I come up with 48(sqrt(3)) mm2 You can also use the fact that radius=side length x (sqrt3)/4 and solve for side length. This gives you side length = 3(radius) divided by square root of 3. Once again, you have side length is 8(sqrt 3) One last method. Once you found side length is 8(sqrt 3) you know that height or altitude of the triangle is 12. Now use 1/2 base x height and you have the exact same answer. Or, The apothem of an equilateral triangle is 1/3 of the median, which is also the height of the triangle. So the height is 12 mm (4 x 3). In one of the right triangles that are formed by drawing the height, we have: one half of the base = cot 60 degrees x height base = 2(cot 60 degrees x height) So that the area of the triangle is: A = (base x height)/2 A = [2(cot 60 degrees x height)(height)]/2 A = cot 60 degrees x height2 A = cot 60 degrees x (12 mm)2 A = 83.14 mm2 (approximately)
0.5*7*13 = 45.5 square mm
A= 22.365mm squared
The base of the triangle is 6 mm because its area is 0.5*6*12 = 36 square mm
The hypotenuse of a triangle with a base of 300 mm and 500 mm height is: 583.1 mm
38.4 sq. mm
It is: 0.5*6*8 = 24 square mm
(19.5 x 6.9)/2 = 67.275 sq mm
5.6 mm Check: 1/2*5.6*1.4 = 3.92 mm2
Area of a rectangle is length x height In this case it is 112 x 30 square mm Do the multiplication and you will have the answer you need
Volume of a pyramid = 1/3*base area*height Volume = 250,000 cubic mm
111.6 A= 0.5 x 18.6 millimeters x 12.0 millimeters
You haven't given enough information. What kind of polygon is it?
If the shape is a triangle, then the area is approx 36.7 square mm.