First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces.

Then find the area of the divisions.

Answer:

The figure will have  2 triangles and 2 rectangles .

The triangles have a combined area of  12  m2.

The rectangles have a combined area of  25  m2.

The figure has a total area of  37 m2.

The figure will have a triangle ABC, a triangle ACD, and a rectangle GDFE.

The total area of the triangles = 26 m²

The total area of the rectangles = 12 m²

The total area of the figure = 38 m²

Given,

The figure is given.

We need to complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces.

Area of a triangle: 1/2 x base x height

Area of a rectangle: length x width

We have,

Two triangles and one rectangle.

                        E__3__F

                         |.          |

                         |           | 4m

        _A_4m_G|_____| D

      /.  |   \.                    /

    /.    |     \.                /
   /     4      \.             /                                          

 /.       |        \.         /

/.         |          \.    /

B.        6m         C.            

Area of triangle ABC

= 1/2 x 6 x 4

= 12 m²

Area of triangle ACD.

= 1/2 x 7 x 4

= 14 m²

The total area of the triangles.

= 12 + 14

= 26 m²

Area of the rectangle EFDG

= 4 x 3

= 12 m²

The total area of the figure.

= 26 + 12

= 38 m²

Thus,

The figure will have a triangle ABC, a triangle ACD, and a rectangle GDFE.

The total area of the triangles = 26 m²

The total area of the rectangles = 12 m²

The total area of the figure = 38 m²

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