48
The area of a triangle
Textbook, pp. 213–216
GoalKnow and use the formula for the area of a triangle.
New words
area of a triangle · uchburchak yuzibase · asosheight (altitude) · balandlikleg of a right triangle · katet
Explanation
The area of a triangle is half the product of a base and the height drawn to it: S = (1/2) · a · h. The height is the perpendicular dropped from a vertex to the opposite side (or its extension). In a right triangle the legs are perpendicular, so S = (1/2) · a · b, where a and b are the legs. From the formula we can find an unknown: h = 2S : a. Triangles with the same base and the same height have equal areas even if their shapes differ.
Worked examples
a = 10 cm, h = 6 cm: S = 10 · 6 : 2 = 30 cm².
If the area is 36 cm² and the base is 9 cm, the height is h = 2 · 36 : 9 = 8 cm.
Class activity
“Turn a triangle into a rectangle”: a paper triangle is folded twice into a rectangle. Pupils see that the rectangle area (base · half the height) equals the triangle's area.
Practice
1
What is the area in cm² of a triangle with base 14 cm and height 5 cm?
35
2
Find the area in cm² of a right triangle with legs 9 cm and 12 cm.
54
3
A triangle has area 48 cm² and height 8 cm. What is its base in cm?
12
4
Why do two triangles with the same base and height have the same area?
The area depends only on base and height: S = a · h : 2. If the apex moves but the height stays the same, the area does not change.