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Final review: geometry
Textbook, p. 233
GoalReview the geometry material: triangles, shapes on squared paper, the circle and the disc.
New words
area of a triangle · uchburchak yuziPick's formula · Pik formulasicircumference · aylana uzunligiarea of a disc · doira yuzi
Explanation
The angles of a triangle sum to 180°; the perimeter is the sum of its sides; the area is S = (1/2) · a · h, and in a right triangle S = (1/2) · a · b (the legs). Any side is smaller than the sum of the other two. The area of a parallelogram is S = a · h. On squared paper the area of a polygon with vertices at lattice points follows Pick's formula: S = M/2 + N − 1 (M boundary points, N interior points). The circumference is C = 2πr = πd, the area of a disc is S = πr², with π ≈ 3.14. Areas are measured in square units: cm², m².
Worked examples
Triangle: a = 12 cm, h = 9 cm: S = 12 · 9 : 2 = 54 cm². A triangle with sides 3 and 4 cannot have a third side 8, since 3 + 4 < 8.
Circle r = 4 cm: C = 2 · 3.14 · 4 = 25.12 cm; area of the disc S = 3.14 · 4² = 50.24 cm².
Class activity
“Geometry workshop”: groups measure classroom objects (books, a lid, a set square), calculate the perimeter, area or circumference and present the result on a poster.
Practice
1
What is the area in cm² of a triangle with base 12 cm and height 9 cm?
54
2
Find the circumference of a circle with radius 7 cm (π = 3.14).
43.96 cm
3
A polygon has 10 boundary and 6 interior lattice points. What is its area?
10
4
Why is area measured in cm² and perimeter in cm?
Perimeter is a length (along a line), while area is a surface made of square units.