Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can find the area of a regular polygon by decomposing it into triangles.
Key words
Regular Polygon — A shape where all sides and all angles are equal.
Decompose — To break a shape into smaller, simpler shapes.
Triangle — A shape with three sides.
Composite — Made by putting two or more simple shapes together.
Formula — A math rule written with symbols.
Steps
My hexagon has 6 equal sides. Each side is 6 feet, and each center triangle has a height of 5.2 feet.
First I find one triangle: A = ½ × base × height = ½ × 6 × 5.2.
I multiply: 6 × 5.2 = 31.2, then ½ × 31.2 = 15.6 square feet.
A hexagon has 6 sides, so it has 6 equal triangles.
I multiply: 6 × 15.6 = 93.6. So the total area is 93.6 square feet.
Try it
A regular pentagon is decomposed into 5 triangles from its center. Each triangle has a base of 7 inches and a height of 4.8 inches. What is the total area of the pentagon?
Check your answer
84 sq in
One triangle: A = 1/2 x 7 x 4.8 = 16.8 sq in. Total = 5 x 16.8 = 84 square inches.
Sentence starter
I know ___ because ___.
Goal: I can explain my steps using the words regular polygon, decompose, triangle, and composite.