3
Problems on the perimeter and area of geometric figures
Textbook: pp. 13–17
GoalUse the perimeter and area formulas of the square, rectangle, triangle, parallelogram, trapezoid and circle to solve practical problems.
New words
perimeter · perimetrarea · yuzbase and height · asos va balandlikcircumference · aylana uzunligi
Explanation
The square has perimeter P = 4a and area S = a²; the rectangle has P = 2(a + b) and S = ab. The area of a triangle is S = ½·a·h, of a parallelogram S = a·h, of a trapezoid S = (a + b)/2 · h, where h is the height. For a circle of radius r the circumference is C = 2πr and the area is S = πr². The area of a complex figure can be found by cutting it into simple figures or by subtracting an extra part from a larger figure. All lengths must be in the same unit, and area is expressed in square units.
Worked examples
A trapezoid has bases 9 cm and 5 cm and height 6 cm: S = (9 + 5)/2 · 6 = 42 cm².
A circle of radius 4 cm: C = 2π·4 = 8π cm and S = π·4² = 16π cm².
Class activity
“Yard plan”: on squared paper draw an L-shaped yard, split it into two rectangles in two different ways, find the total area each way and compare.
Practice
1
A rectangular plot is 7 m wide and 12 m long. What is its perimeter (m)?
38
2
A triangle has base 14 cm and height 9 cm. What is its area (cm²)?
63
3
A parallelogram has area 96 cm² and base 12 cm. What is its height (cm)?
8
4
Why do we halve the sum of the bases in the trapezoid area formula?
The midline of a trapezoid is half the sum of the bases, and the area equals the midline times the height.