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Area of parallelograms and triangles

الأسبوع 26 · مساحة متوازي الأضلاع والمثلث القائم الزاوية · 3 دروس
2

Area of a right-angled triangle as half a rectangle

Discover Mathematics P6: Term 2, Unit 12, Lessons 1–2
GoalFind the area of a right-angled triangle as half a rectangle, and of any triangle as base × height ÷ 2.
New words
right-angled triangle · a triangle with one right anglehalf · one of two equal partsleg · one of the two sides that make the right angle
Explanation

Draw a right-angled triangle and complete a rectangle around it. The rectangle is cut by its diagonal into two equal right triangles, so each triangle is half of the rectangle. The sides of the rectangle are the two legs of the triangle, so the area of the triangle is leg × leg ÷ 2. In a right triangle one leg is the base and the other is the height. For any triangle, area = base × height ÷ 2, where the height is the perpendicular distance from the base to the opposite corner. The longest side of a right triangle is not a height.

ƒFormula
Area of a triangle = base × height ÷ 2 A = b × h ÷ 2
Worked examples
8 cm6 cmABC
A right triangle has legs 6 cm and 8 cm. It is half of a rectangle 6 by 8, whose area is 48 cm². So the triangle has area 48 ÷ 2 = 24 cm².
A right triangle has legs 5 cm and 12 cm and a long side of 13 cm. The height is the other leg, not 13. Area = 5 × 12 ÷ 2 = 30 cm².
Compare. A parallelogram with base 8 cm and height 4 cm has area 32 cm². A triangle with the same base and height has area 8 × 4 ÷ 2 = 16 cm², exactly half.
Class activity

Half a rectangle. Draw a rectangle on squared paper and cut it along a diagonal. Check that the two triangles fit on top of each other. Count the squares in one triangle.

Practice
1
A right triangle has legs 10 cm and 4 cm. Find its area.
2
A right triangle has legs 9 m and 12 m. Find its area.
3
A triangle has base 14 m and height 5 m. Find its area.
4
A right triangle is half of a rectangle 9 cm by 6 cm. Find the area of the triangle.
5
A right triangle has legs 6 cm and 8 cm and a long side of 10 cm. Karim writes 6 × 10 ÷ 2 = 30. What is wrong? Give the area.