114
Completing shapes to a rectangle
Textbook: Part 4, lesson 114, pp. 19–21
GoalCompleting shapes to a rectangle: area of a right triangle, area of a polygon by subtracting the extra parts.
New words
right triangle · to‘g‘ri burchakli uchburchakleg · katetcompleting · to‘ldirishextra part · ortiqcha qism
Explanation
If we complete a right triangle to a rectangle with sides equal to the legs, the triangle's area is half of the rectangle's: S = leg × leg : 2. To find the area of a polygon, put it inside a rectangle, find the rectangle's area and subtract the extra triangles around it. The same works on a coordinate grid.
Worked examples
Legs 8 cm and 5 cm: S = 8 × 5 : 2 = 20 cm².
An octagon in an 8 × 6 rectangle with four corner triangles (legs 2 and 3) cut off: 48 − 4 × 3 = 36.
Class activity
“Cut and see”: children complete a triangle to a rectangle on squared paper and, cutting with an adult's help, check that the extra triangles fit together or form half.
Practice
1
What is the area in cm² of a right triangle with legs 8 cm and 5 cm?
20
2
From each corner of an 8 cm × 6 cm rectangle a triangle with legs 2 cm and 3 cm is cut off. What is the area of the rest in cm²?
36
3
On a coordinate grid A(0; 0), B(6; 2) and C(2; 6) form a triangle. Find its area by subtracting 3 extra right triangles from a 6 × 6 square.
16
4
A right triangle has area 15 cm² and one leg 5 cm. How many cm is the other leg?
6
5
A square handkerchief with side 16 cm is folded along a diagonal. What is the area in cm² of the triangle formed?
128