Decompose the rectangle along the diagonal and recompose the two pieces to make a different shape

Decompose the rectangle along the diagonal and recompose the two pieces to make a different shape, then five different ways are shown.

Area is the number of squares inside a two-dimensional shape.

Here are two important principles for finding area:

A rectangle has two diagonals. Each one is a line segment drawn between the opposite vertices (corners) of the rectangle. For rectangle, shapes can be decomposed and rearranged back to rectangles to find the area.  When decomposing and rearranging shapes the area of the polygon does not change.

The rectangle is shown in the picture below. After decompose the rectangle along the diagonal, we can varied the pieces to make various different shape. Picture below also shown the five different ways pieces from the rectangle.

Grade:  9

Subject:  Mathematics

Chapter:  Area and Surface Area

Keywords: Area, Surface Area, Decomposing, Rearranging, rectangle

the answer is 175.4379

step-by-step explanation: