To solve word problems about the area and perimeter of different shapes, you need to know some basic formulas. These formulas help you figure out the measurements for each shape.

Key Formulas

1. Square

   • Area: ( A = s^2 ) where ( s ) is the length of one side.
   • Perimeter: ( P = 4s ).

2. Rectangle

   • Area: ( A = l \times w ) where ( l ) is the length and ( w ) is the width.
   • Perimeter: ( P = 2(l + w) ).

3. Triangle

   • Area: ( A = \frac{1}{2} \times b \times h ) where ( b ) is the base and ( h ) is the height.
   • Perimeter: ( P = a + b + c ) where ( a ), ( b ), and ( c ) are the lengths of the sides.

4. Circle

   • Area: ( A = \pi r^2 ) where ( r ) is the radius.
   • Circumference (like perimeter): ( C = 2\pi r ).

Steps to Solve Word Problems

1. Read the Problem Carefully: Look for the shape mentioned and the numbers given (like length and width).

2. Identify Required Values: Decide if you need to find area, perimeter, or both.

3. Choose the Right Formula: Pick the correct formula based on the shape you are working with.

4. Substitute Values: Put the numbers from the problem into the formula.

5. Perform Calculations: Do the math to find the area or perimeter.

6. Review Your Answer: Check if your answer makes sense. For example, make sure the area is a positive number and matches the dimensions you used.

Example Problem

Problem: Find the area and perimeter of a rectangle that has a length of 10 cm and a width of 5 cm.
Solution:

• Area: ( A = l \times w = 10 \times 5 = 50 \text{ cm}^2 )
• Perimeter: ( P = 2(l + w) = 2(10 + 5) = 30 \text{ cm} )

By following these steps and using the formulas, you can easily solve word problems about area and perimeter!