Find the area of the regular shape with the given apothem 10cm. round to the nearest tenth
To find the area of a regular polygon, you can use the formula:
Area = (1/2) * Perimeter * Apothem
Since the apothem is given as 10cm, and the perimeter is not provided, we cannot directly calculate the area with this formula.
However, we can utilize trigonometry to find the area of a regular polygon with the given apothem. For example, if we assume the regular shape is an octagon (8 sides), we can divide the octagon into 8 congruent isosceles triangles with a base of 10cm and angles of 45 degrees.
By splitting each triangle in half into a right-angled triangle, we can find the base and height of this right-angled triangle by using the sine and cosine functions:
sin(45 degrees) = height / 10cm
cos(45 degrees) = base / 2
Height = 10cm * sin(45 degrees) = 7.1cm
Base = 2 * 10cm * cos(45 degrees) = 14.1cm
Now, the area of one of these triangles is:
Area of one triangle = (1/2) * base * height
Area of one triangle = (1/2) * 14.1cm * 7.1cm = 50.1 cm²
Since the octagon comprises 8 such triangles, the total area of the octagon is:
Area = 8 * 50.1 cm² = 400.8 cm²
Therefore, the area of the regular shape with an apothem of 10cm is approximately 400.8 cm².