6.G.A.1 6th Grade Geometry

Area of Polygons

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing or decomposing them into known shapes.

How to explain it

At this standard, students find the area of right triangles, general triangles, parallelograms, trapezoids, and composite polygons by identifying base and perpendicular height and applying the correct area formula.

The anchor students hold onto: To find the area of a polygon, identify the base and perpendicular height, then apply the correct formula for the shape.

Area of polygons (6.G.A.1) connects to finding volume of prisms with fractional edge lengths in Sheet #32.

Worked examples

Example 1 Right Triangle

Find the area. b=6 cm, h=8 cm.

Step 1A = 1/2 x base x height

Step 2A = 1/2 x 6 x 8

Step 3A = 1/2 x 48

Step 4A = 24 sq cm

Answer24 sq cm

Example 2 General Triangle

Find the area. b=10 m, h=4 m.

Step 1A = 1/2 x base x height

Step 2A = 1/2 x 10 x 4

Step 3A = 1/2 x 40

Step 4A = 20 sq m

Answer20 sq m

Common mistakes

What students write Student uses A = b x h (parallelogram formula) for a triangle, forgetting the 1/2 factor — common error when switching between shape types on the same assignment.

The fix A triangle is exactly HALF of a parallelogram with the same base and height. The formula is A = 1/2 x b x h. Always check: is this a triangle? If yes, multiply by 1/2.

What students write Student uses the slant side (hypotenuse or oblique side) of a triangle or parallelogram as the height instead of the perpendicular distance from base to opposite vertex.

The fix Height must be perpendicular (90°) to the base. Draw a dashed line from the base straight up to the opposite vertex — that vertical distance is the height, not the slant side.

Teacher tip

Head off the two predictable errors before they happen. First: A triangle is exactly HALF of a parallelogram with the same base and height. The formula is A = 1/2 x b x h. Always check: is this a triangle? If yes, multiply by 1/2. Second: Height must be perpendicular (90°) to the base. Draw a dashed line from the base straight up to the opposite vertex — that vertical distance is the height, not the slant side.