inches; 3 feet = 36 inches). The area of the board would be 48 inches x 36 inches or 1728 inches2 . The area of one index card is 12 inches2 . Divide 1728 inches2 by 24 inches2 to get the number of index cards. 72 index cards would be needed. Q: Find the area of the trapezoid shown below using the formulas for rectangles and triangles. Solution: The trapezoid could be decomposed into a rectangle with a length of 7 units and a height of 3 units. The area of the rectangle would be Rhombus – b x h or d1 x d2 Kites - d1 x d2 21units2. The triangles on each side would have the same area. 2 2 The height of the triangles is 3 units. After taking away the middle rectangle’s base length, Decompose/Compose (Triangles) there is a total of 5 units remaining for both of the side triangles. The base length of each triangle is half of 5. The Trapezoids - ½ h (a + b) base of each triangle is 2.5 units. The area of one triangle Trapezoids can be decomposed into triangles and rectangles (see would be ½ (2.5 units)(3 units) figures below). Using the trapezoid’s dimensions, the area of the or 3.75 units2 . Using this individual triangle(s) and rectangle can be found and then added information, the area of the together. trapezoid would be: 21 units2 + 3.75 units2 +3.75 + units2 = 28.5 units2 Irregular Polygon – cut into rectangles/triangles and add the areas together
inches; 3 feet = 36 inches). The area of the board would be 48 inches x 36 inches or 1728 inches2 . The area of one index card is 12 inches2 . Divide 1728 inches2 by 24 inches2 to get the number of index cards. 72 index cards would be needed. Rhombus – b x h or d1 x d2 Kites - d1 x d2 2 2 Decompose/Compose (Triangles) Trapezoids - ½ h (a + b) Trapezoids can be decomposed into triangles and rectangles (see figures below). Using the trapezoid’s dimensions, the area of the individual triangle(s) and rectangle can be found and then added together. Irregular Polygon – cut into rectangles/triangles and add the areas together Q: Find the area of the trapezoid shown below using the formulas for rectangles and triangles. Solution: The trapezoid could be decomposed into a rectangle with a length of 7 units and a height of 3 units. The area of the rectangle would be 21units2. The triangles on each side would have the same area. The height of the triangles is 3 units. After taking away the middle rectangle’s base length, there is a total of 5 units remaining for both of the side triangles. The base length of each triangle is half of 5. The base of each triangle is 2.5 units. The area of one triangle would be ½ (2.5 units)(3 units) or 3.75 units2 . Using this information, the area of the trapezoid would be: 21 units2 + 3.75 units2 +3.75 + units2 = 28.5 units2