What are the formulas for the area of a rectangle, square, triangle, parallelogram, and trapezoid?
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To find the formulas for the area of different shapes, we need to know the necessary measurements for each shape. Here are the formulas for the area of a rectangle, square, triangle, parallelogram, and trapezoid:
1. Rectangle:
The area of a rectangle is given by the formula: A = length × width, where "A" represents the area, "length" represents the length of the rectangle, and "width" represents the width of the rectangle.
2. Square:
In a square, all sides are equal, so the formula for the area is simply: A = side², where "A" represents the area, and "side" represents the length of any side of the square.
3. Triangle:
The area of a triangle can be calculated using different formulas depending on the given measurements. Here are two common formulas:
- If you know the length of the base (b) and the height (h), then the area can be calculated using the formula: A = (1/2) × base × height, where "A" represents the area, "base" represents the length of the base, and "height" represents the altitude or height of the triangle.
- If you know the lengths of all three sides (a, b, c), then you can use Heron's formula to calculate the area: A = √(s(s - a)(s - b)(s - c)), where "A" represents the area, and "s" represents the semiperimeter of the triangle given by s = (a + b + c)/2.
4. Parallelogram:
The area of a parallelogram is given by the formula: A = base × height, where "A" represents the area, "base" represents the length of the base of the parallelogram, and "height" represents the altitude or height of the parallelogram.
5. Trapezoid:
The area of a trapezoid can be calculated using the formula: A = (1/2) × (b1 + b2) × h, where "A" represents the area, "b1" and "b2" represent the lengths of the two parallel bases, and "h" represents the altitude or height of the trapezoid.
Remember to use the appropriate units when using these formulas.