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Area of triangles, parallelograms & trapezoids

Measurement

Japanese school year: Elementary 5

What you learn

Learn the geometric formulas to calculate the areas of triangles, parallelograms, and trapezoids using base and height. These formulas are useful in carpentry, land measurement, and design projects. Prior knowledge of rectangle area calculation along with perpendicular and parallel lines will help in understanding the derivations.

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Key points

This formula finds the area S of a triangle. Multiply the base a by the height h, then divide by 2.

S=12ahS = \frac{1}{2}ah

This formula finds the area S of a parallelogram. Multiply the base a by the height h.

S=ahS = ah

This formula finds the area S of a trapezoid. Add the top base a and bottom base b, multiply by height h, then divide by 2.

S=12(a+b)hS = \frac{1}{2}(a + b)h

This formula finds the area S of a rhombus. Multiply the lengths of the two diagonals x and y, then divide by 2.

S=12xyS = \frac{1}{2}xy

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