Figure It Out
Task: Find the areas of the figures on the grid by dividing them into rectangles and triangles.
(Note: Grid squares are assumed to be 1 unit).
Figure a (Parallelogram-like):
- Base = 4 units. Height = 6 units.
- Area = sq units.
Figure b (Trapezoid/Triangle combo):
- Decompose into a central rectangle and side triangles.
- Solution says: 30 sq units.
Figure c (Complex Polygon):
- Solution says: 48 sq units.
Figure d (M-shape/Polygon):
- Solution says: 16 sq units.
Figure e (Diamond/Kite):
- Solution says: 12 sq units.
- Calculation: Box it in a rectangle of . The diamond usually takes up half the area of the bounding box if vertices touch the midpoints/sides. .
Tip
Method: To solve these on grid paper:
- Draw a bounding rectangle around the shape.
- Calculate the area of the bounding rectangle.
- Calculate the areas of the empty triangles in the corners (using ).
- Subtract the corner areas from the bounding box area.