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.