Prerequisite for problems 1-3: Understanding the
derivation of area of triangles.
9 cm2
1) Given four triangles formed in a rectangle, having a
common point inside of the rectangle, as shown on the
right. What is the area of the triangle?
8 cm2
4 cm2
?
Alternative:
1(alt): The ratio of the areas of the two shaded triangles is 2:1 (or 8:4), what is the ratio of the
two unshaded triangles?
2) What fraction of the rectangle is
unshaded?
If this can not be determined, identify the
missing information that may be needed
answer the question.
2 (alt): If the ratio of the heights of the
triangles on the upper side to the
lower side is 3:5, what fraction of
the rectangle is unshaded?
A
3) The area of the rectangle ABCD on the
right is 140 cm2. The area of the triangle
Δ DXY is 20 cm2. What is the area of
the shaded portion of the rectangle?
X
Z
B
20 cm2
Y
D
C
Prerequisite for problem 4: Pattern to systematically
identify different triangles. (For a large number of
triangles, addition of sequence of numbers.)
4) The triangle on the right is made from three triangles
stacked up as shown below.
+
+
For the triangle on the right, how many
different triangles are stacked up
together? (How many different triangles
can be seen?
A
4 cm
D
5) Two identical right triangles
12 cm
are displaced with respect to
each other by 5 cm in the
horizontal direction (as shown
on the right). (Note: The
C
B
5 cm
triangles are not drawn to
scale.) The height of both of
the triangle is 12 cm. Distance AD is 4 cm. What is the area of the shaded portion ABCD of
the displaced triangle?
Prerequisite for problem 5: Understanding the area of triangles, similar triangles, fraction
multiplications, and ratios.