What are the formulas for the perimeter and area of a trapezium, rectangle, and square? Explain in a way that a 6th-grade student can understand.
Understand the Problem
The question asks for the formulas to calculate the perimeter and area of a trapezium (also known as a trapezoid), a rectangle, and a square. The explanation should be at a level understandable for a 6th-grade student.
Answer
Trapezium: $P = a + b + c + d$, $A = \frac{1}{2} \times (a + b) \times h$ Rectangle: $P = 2(l + w)$, $A = l \times w$ Square: $P = 4s$, $A = s^2$
Answer for screen readers
Trapezium: Perimeter: $P = a + b + c + d$ Area: $A = \frac{1}{2} \times (a + b) \times h$
Rectangle: Perimeter: $P = 2(l + w)$ Area: $A = l \times w$
Square: Perimeter: $P = 4s$ Area: $A = s^2$
Steps to Solve
- Trapezium Perimeter
The perimeter of any shape is the sum of all its sides. For a trapezium, you simply add the lengths of its four sides.
Let's say the sides of the trapezium are $a$, $b$, $c$, and $d$. Then the perimeter is:
$P = a + b + c + d$
- Trapezium Area
The area of a trapezium is calculated using the formula:
$A = \frac{1}{2} \times (a + b) \times h$
Where $a$ and $b$ are the lengths of the two parallel sides, and $h$ is the perpendicular height (the distance between the parallel sides).
- Rectangle Perimeter
A rectangle has two pairs of equal sides. We usually call the longer side the "length" ($l$) and the shorter side the "width" ($w$). The perimeter is the sum of all sides:
$P = l + w + l + w = 2l + 2w = 2(l + w)$
- Rectangle Area
The area of a rectangle is found by multiplying its length and width:
$A = l \times w$
- Square Perimeter
A square is a special type of rectangle where all four sides are equal. If we call the length of one side "s", then the perimeter is:
$P = s + s + s + s = 4s$
- Square Area
The area of a square is found by multiplying the length of one side by itself:
$A = s \times s = s^2$
Trapezium: Perimeter: $P = a + b + c + d$ Area: $A = \frac{1}{2} \times (a + b) \times h$
Rectangle: Perimeter: $P = 2(l + w)$ Area: $A = l \times w$
Square: Perimeter: $P = 4s$ Area: $A = s^2$
More Information
A trapezium is called a trapezoid in the US. A square is a special type of rectangle, but a rectangle is not a special type of square!
Tips
A common mistake is using the wrong height when calculating the area of a trapezium. Make sure to use the perpendicular height (the shortest distance) between the parallel sides, not the length of one of the non-parallel sides. Also, remembering the area formula for a trapezium can be tricky, so practice it a few times!
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