6.G.1 — Area of parallelograms.
Step 01 of 04
Parallelogram area formula.
A=b×h
where b is the length of the BASE and h is the PERPENDICULAR HEIGHT (NOT the slanted side).
Step 02 of 04
Why? A parallelogram can be cut and rearranged into a RECTANGLE with the same base and height. So same area as a rectangle: base × height.
Step 03 of 04
Worked example. Parallelogram with base 10 cm and perpendicular height 4 cm.
A=10×4=40 sq cm
Step 04 of 04
Watch the height! The slanted side of the parallelogram is the SIDE LENGTH, not the height. The HEIGHT is measured perpendicular to the base.
Key insight
Parallelogram area = base × perpendicular HEIGHT. Side length is NOT height. Same as rectangle area logic.
6.G.2 — Area of triangles.
Step 01 of 04
Triangle area formula.
A=21×b×h
Half the base times the perpendicular height. Half a parallelogram (you can put two identical triangles together to make a parallelogram).
Step 02 of 04
Worked example. Triangle with base 8 cm, height 5 cm.
A=21(8)(5)=20 sq cm
Step 03 of 04
Same height-not-side trap. Like with parallelograms, the HEIGHT is perpendicular to the base. If you're given a slanted side, it's NOT the height.
Step 04 of 04
Right triangles are easy: the two legs are the base and height. A=21⋅leg1⋅leg2.
Key insight
Triangle area = half × base × HEIGHT (perpendicular to base). For right triangles, the legs serve as base and height directly.
6.G.3 — Area of composite figures.
Step 01 of 04
A composite figure is built from simpler shapes (rectangles, triangles, parallelograms). Find the area of each piece, then ADD.
Step 02 of 04
Worked example. An L-shape: 8 × 4 rectangle on top of a 5 × 3 rectangle.
A=8×4+5×3=32+15=47 sq units
Step 03 of 04
Subtract for "missing" pieces. If a rectangle has a triangular notch cut out, compute the rectangle's area and SUBTRACT the triangle's area.
Step 04 of 04
Pick a clean split. Different splits give the same total — choose the one with simplest dimensions.
Key insight
Composite figure → split into known shapes → compute each → add. Or compute the bounding shape and SUBTRACT the missing part. Either approach works.
6.G.4 — Polygons on the coordinate plane.
Step 01 of 04
Find side lengths of polygons on the coordinate plane using the distance technique: same row/column → absolute difference of the other coordinate.
Step 02 of 04
Worked example. Quadrilateral with vertices A(1, 1), B(7, 1), C(7, 5), D(1, 5).
| AB | →horizontal — |7 − 1| = 6 |
| BC | →vertical — |5 − 1| = 4 |
| CD | →|7 − 1| = 6 |
| DA | →|5 − 1| = 4 |
Two pairs of equal opposite sides → rectangle. Area = 6×4=24 sq units.
Step 03 of 04
Triangles on a grid. Use the base and height directly from the grid, then apply A=21bh.
Step 04 of 04
Word problem context. A rectangular garden has corners at (0, 0), (10, 0), (10, 6), (0, 6). Perimeter and area?
P=2(10)+2(6)=32 units
A=10×6=60 sq units
Key insight
Coordinate planes give exact dimensions. Use absolute differences for horizontal / vertical sides. Apply standard area formulas to the resulting rectangles, triangles, etc.