Grade 5 (age 10-11)

grade 5 Area of Polygons

Area of Polygons

You find a polygon's area by turning it into a rectangle you already know how to measure. A parallelogram becomes a rectangle, so its area is base times height; two matching triangles make a parallelogram, so a triangle is base times height divided by 2; a trapezoid splits into two triangles. Change the base and the height and each shape is cut and rearranged until its area is set.

Core Idea for Finding Area

✂️ Cut and rearrange into a rectangle!

①Every polygon can be turned into a rectangle to find its area. The cut-and-paste picture is in the next step, where you change base and height

②Parallelogram: cut a triangle and stick it on → base × height

③Triangle: two copies make a parallelogram, so divide by 2

④A trapezoid splits into two triangles: (a+b)×height÷2. Top 4, bottom 6, height 4 → (4+6)×4÷2=20

Area of Parallelograms

Base8

Height5

Area of Triangles

↔️ Same base and height

The base and height sliders above also drive this triangle.

💡 Triangle = half of a rectangle

①Two same triangles → parallelogram

②That's why we divide by 2

③Finding base and height is the key!

Summary

Parallelogram Area

Area = base × height

Cut the triangle to form a rectangle

Triangle Area

Area = base × height2

Half of a rectangle = triangle

Trapezoid Area

Area = (top + bottom) × height2

Split into two triangles

🎯 Key Points

①Rectangle area = width × height (basic!)

②Parallelogram = base × height

③Triangle = base × height ÷ 2

④Trapezoid = (top+bottom) × height ÷ 2

⑤Height is always perpendicular to the base

Examples and Unit Test

Example 1

Find the area of a parallelogram with base 8 cm and height 5 cm.

Area of a parallelogram = base × height.

8 × 5 = 40, so the area is 40 cm².

▸ 40 cm²

A parallelogram becomes a rectangle when you cut a triangle off, so area = base × height.

Example 2

Find the area of a triangle with base 8 cm and height 5 cm.

Area of a triangle = base × height ÷ 2.

8 × 5 ÷ 2 = 40 ÷ 2 = 20, so the area is 20 cm².

▸ 20 cm²

A triangle is half of a parallelogram, so we divide by 2.

Unit Test

What is the area of a trapezoid with top 4 cm, bottom 6 cm, and height 4 cm?

①20 cm²

②40 cm²

③24 cm²

④10 cm²

▸ ① 20 cm²

Area of a trapezoid = (top + bottom) × height ÷ 2.

(4 + 6) × 4 ÷ 2 = 10 × 4 ÷ 2 = 40 ÷ 2 = 20 cm².

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Congruence & Symmetry

Rectangular Solid: Surface Area & Volume