How much flat space does a shape cover? Learn the formulas for finding the area of rectangles and triangles, see how the two are connected, and practice on real shapes.
Area is the amount of flat space inside a two-dimensional shape. We measure area in square units — like square inches, square feet, or square centimeters — because we're really asking: how many 1-unit-by-1-unit squares would it take to completely cover the shape?
When you see a unit like in² (square inches) or cm² (square centimeters), that little "2" means the same unit is multiplied by itself — because you're covering a flat surface with squares, not measuring a single length.
A rectangle is made of neat rows and columns of unit squares, so its area formula is simple: multiply the base (length) by the height (width).
base = 6 units, height = 4 units
6 × 4 = 24
Area = 24 square units
It doesn't matter which side you call "base" and which you call "height" — 6 × 4 gives the same answer as 4 × 6. Multiplication works in either order.
Here's the key idea: a triangle is exactly half of a rectangle with the same base and height. So the triangle formula starts the same way as the rectangle's, then cuts the answer in half.
Which just means: multiply base and height, then take half.
base = 8 units, height = 5 units
8 × 5 = 40
Half of 40 = 20
Area = 20 square units
The height of a triangle is never measured along a slanted side — it's always the straight perpendicular distance from the base up to the opposite corner (the apex). For some triangles, that means picturing the base stretched out a little, like the dashed line above.
Use the base and height shown to calculate the area of each shape. Remember: rectangles use base × height, and triangles use half of base × height.
Calculate the area, then type your answer below.