# how many different shapes can you make with the 4 triangles cut from this rectangle? how do you know?

Rectangle
Square
Trapezium

## To determine the number of different shapes you can make with the 4 triangles cut from a rectangle, we need to consider various arrangements and combinations. Let's go step-by-step:

Step 1: Identify the possible orientations of the triangles.
The four triangles can be arranged in different orientations: upright, upside-down, flipped horizontally, and flipped vertically.

Step 2: Reflect on the possible positions of the triangles.
Each triangle can be placed at four different positions within the rectangle: top-left, top-right, bottom-left, and bottom-right. This applies to each of the four orientations.

Step 3: Calculate the total number of possible shapes.
Considering the number of orientations (4) and positions for each triangle (4), the total number of possible arrangements can be calculated as:
Total shapes = Number of orientations ^ Number of triangles
Total shapes = 4 ^ 4
Total shapes = 256

Therefore, you can make 256 different shapes by arranging the four triangles cut from the rectangle in various orientations and positions.

## To determine how many different shapes you can make with the four triangles cut from the rectangle, you need to understand the concept of combinations.

First, let's consider the four triangles. When arranging them, you can use each triangle as either an upright or inverted shape. So, for each triangle, you have two options.

Since there are four triangles, you'll have 2 options for the first triangle, 2 options for the second triangle, 2 options for the third triangle, and 2 options for the fourth triangle. To find the total number of combinations, you multiply all the options together: 2 x 2 x 2 x 2 = 16.

Therefore, there are 16 different shapes you can make by arranging the four triangles cut from the rectangle.