the perimeter of a quadrilateral is 30 cm. what is the maximum possible area of the quadrilateral.
max area is when the figure is a square
To find the maximum possible area of a quadrilateral, we need to determine the shape that will maximize the area given the perimeter constraint. Let's break it down step by step:
1. Start by considering different types of quadrilaterals. Some examples include rectangles, squares, parallelograms, trapezoids, and rhombuses.
2. Recall that the perimeter of a quadrilateral is the sum of all its side lengths. In this case, the perimeter is given as 30 cm.
3. Since we want to find the maximum possible area, we need to consider the quadrilateral that will utilize the entire perimeter and maximize the enclosed area.
4. One way to approach this is to consider a square. This is because a square is a special case of a rectangle with all sides equal.
5. To find the side length of the square, divide the given perimeter (30 cm) by 4. 30 cm ÷ 4 = 7.5 cm. Therefore, each side of the square measures 7.5 cm.
6. Finally, calculate the area of the square using the formula A = s^2, where A is the area and s is the side length:
A = 7.5 cm × 7.5 cm = 56.25 cm^2.
Thus, the maximum possible area of the quadrilateral, given a perimeter of 30 cm, is 56.25 cm^2 when it is a square with side lengths of 7.5 cm.