Draw a polygon with area equal to 7.5 square units.
Draw a triangle with a height of 3 and a base of 5. Since the area of a triangle is equal to (bh)/2 the area would be (3*5)/2 = 7.5 sq units
To draw a polygon with an area equal to 7.5 square units, you would need to know the number of sides and the lengths of those sides. The formula for calculating the area of a polygon depends on the specific shape. However, for a regular polygon (a polygon with all sides and angles equal), you can use the formula:
Area = (s^2 * n) / (4 * tan(π/n))
where s is the length of each side and n is the number of sides.
For example, let's consider a regular hexagon (a polygon with 6 sides). To find the length of one side, we can divide the total area (7.5 sq units) by the area of each equilateral triangle within the hexagon. An equilateral triangle has all sides equal, so we can use the formula (bh)/2, where b is the base (side length of the hexagon) and h is the height.
Area of each triangle = (base * height) / 2 = (s * s * √3) / 4 (for an equilateral triangle, the height is (s * √3) / 2)
Now, let's solve for s (length of one side):
Area of each triangle = 7.5 / 6 = (s * s * √3) / 4
Multiply both sides by 4 and divide by √3 to isolate s:
s^2 = (4 * 7.5) / (6 * √3)
s^2 ≈ 4.33
s ≈ √4.33 (taking the square root of both sides)
This gives us the length of one side of the hexagon. Now, you can use this length to draw a regular hexagon with an area of 7.5 square units.
Note: There are multiple polygons that can have an area of 7.5 square units, so the shape and size of the polygon you draw may vary depending on the number of sides and their lengths.