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Triangles as Parts of Rectangles

Let us take a rectangle and divide it into two triangles by joining the
opposite vertices (diagonal). If we superpose one triangle on the other,
they are exactly the same in size and overlap with each other.

Thus, we can say both triangles are congruent to each other and having
equal area.

Therefore, the area of the triangle thus formed will be half of the area of the rectangle.
1
So, area of each triangle = × area of the rectangle
2
If the length and the breadth of the rectangle is l and b respectively, then
1
Area of each triangle = × (l × b) sq. units
2
Example 9: A rectangle of sides 8 cm and 4 cm cut into two triangles diagonally. Find the area of
each of the triangle.
Solution: Length of the rectangle, l = 8 cm
8 cm
Breadth of the rectangle, b = 4 cm

1 4 cm 4 cm
Area of each of the triangle = × (l × b)
2
1
= × (8 cm × 4 cm) 8 cm
2

1
= × 32 sq. cm = 16 sq. cm
2
Now, if we take a square and join opposite vertices, then the square is divided into
four congruent triangles having equal area.

1
Thus, area of each triangle = × Area of the square
4
Or
1
Area of each triangle = × a , where ‘a’ denotes the length of side of the square.
2
4
Example 10: A square of side 6 cm is divided into 4 triangles. Find the area of each triangle.
Solution: Length of each side, a = 6 cm 6 cm

1 Quick Check
Area of each triangle = × a 2
4 6 cm 6 cm Find the area of a
1 triangle formed when a
= × (6 cm) 2
4 6 cm rectangle of sides 8 cm

1 and 4 cm is cut into two
= × 36 sq. cm = 9 sq. cm triangles diagonally.
4

285 Perimeter and Area