Area: Step-by-Step Guide
Area tells you how much flat space is inside a shape. We measure it in square units, like square centimeters. For a rectangle, multiply length times width. For a parallelogram, multiply base times height. For a trapezoid, add the two parallel sides, divide by 2, and multiply by the height.
Math Racer skill guide · Elementary · Grades K-5
How to solve it, step by step
- Identify the shape. Decide if the shape is a rectangle, square, parallelogram, trapezoid, or something else. The shape tells you which formula to use.\[\text{rectangle},\;\text{square},\;\text{parallelogram},\;\text{trapezoid}\]
- Write the area formula. Rectangle: area = length x width. Square: area = side x side. Parallelogram: area = base x height. Trapezoid: area = (1/2) x (base 1 + base 2) x height.\[A_{\text{rect}} = lw,\; A_{\text{sq}} = s^2,\; A_{\text{par}} = bh,\; A_{\text{trap}} = \tfrac{1}{2}(b_1 + b_2)h\]
- Put in the measurements. Replace the letters in the formula with the numbers from the problem. Make sure all the measurements use the same unit.\[A = l \times w\]
- Multiply and write the units. Work out the answer. Write it in square units, like square centimeters or square meters.\[A = (l)(w) \;\text{units}^2\]
Worked example
A rectangular garden measures 12 meters by 7 meters. Find its area.
Step 1: The garden is a rectangle.
Step 2: The formula is area = length x width.
Step 3: Put in the numbers: area = 12 x 7.
Step 4: Multiply: 12 x 7 = 84.
Step 5: Add the units: the area is 84 square meters.
Check: Picture 12 rows of 7 little squares. 12 x 7 = 84 little squares in all.
Tips and common mistakes
- Area is always in square units, like square meters. A plain unit like meters is not enough.
- Change all the measurements to the same unit before you multiply.
- For a parallelogram, the height goes straight up from the bottom to the top. It is not the slanted side.
- For a trapezoid, the two parallel sides are the bases. The height is the straight-up distance between them.
- For a strange shape, cut it into simple shapes like rectangles, find each area, and add them.
- A square is a rectangle with equal sides, so area = side x side.
- Estimate to check. A 10 by 7 rectangle has an area of 70, so 84 for a 12 by 7 rectangle makes sense.