Answer :

This polygon is composed of a right triangle and a parallelogram.

The area of right angle :
[tex]A_\Delta=\frac{1}{2}\cdot15\cdot8=\frac{1}{2}\cdot120=\boxed{60\ (cm^2)}[/tex]

The area of the parallelogram:
[tex]A_P=15\cdot(13-8)=15\cdot5=\boxed{75\ (cm^2)}[/tex]

The area of the polygon is equal:[tex]A=A_\Delta+A_P[/tex]

Therefore, the answer is:
[tex]\boxed{\boxed{A=60\ cm^2+75\ cm^2=135\ cm^2}}[/tex]
AL2006

Slice the picture in half, across the middle dotted line.

The top half is a triangle.  Its base is 15cm and its height is 8cm .
Area of a triangle is (1/2) (base x height) = (1/2) (120cm²) = 60 cm².

The bottom half is a parallelogram.  Its base is 15cm and its height is 5cm.
Area of a parallelogram is (base x height) = (15cm x 5cm) = 75 cm².

Add the two pieces together.  (60cm²) + (75 cm²) = 135 cm²

Breathe from the diaphragm, enunciate, and watch the conductor.

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