50
Simple area problems on squared paper
Textbook, pp. 220–221
GoalSolve simple area problems on squared paper: parallelogram and splitting complex shapes.
New words
parallelogram · parallelogrammcomposite shape · murakkab shaklsplitting into parts · bo‘laklarga ajratishunit of area · yuz birligi
Explanation
The area of a parallelogram is the product of a base and the height drawn to it: S = a · h (not with the slanted side!). The reason is that if we move the triangle from one end of a parallelogram to the other end, we get a rectangle. To find the area of a composite shape we split it into rectangles and triangles and add the areas, or we subtract the extra part from a big rectangle. We can check the result with Pick's formula.
Worked examples
Parallelogram: base 9, height 5: S = 9 · 5 = 45 (square units).
L-shape: a 2 × 2 square cut out of a 6 × 4 rectangle: S = 24 − 4 = 20.
Class activity
“Split and calculate”: groups get squared paper with slanted shapes. They split the shape into rectangles and triangles, compute the area and compare two different methods.
Practice
1
A parallelogram has base 9 and height 5. What is its area?
45
2
A 2 × 2 square is cut out of a 6 × 4 rectangle. What is the area of what remains?
20
3
A triangle has a base of 8 squares and a height of 5 squares. What is its area in squares?
20
4
Why can the area of a parallelogram not be base times the slanted side?
The slanted side is longer than the height. It is the height that becomes the width when the parallelogram is rearranged into a rectangle.