Geometry CP Unit 12 Name: __________________________________ Station 1: Area of Parallelograms Recall that a parallelogram is a quadrilateral with opposite parallel sides. Any side of the parallelogram can be considered the base (b). In this parallelogram, we will consider the “bottom” side the base. Any side, however, cannot be the height (h). The height must be perpendicular to the base. It is the distance from a base to an opposite vertex. 1. Locate the parallelogram in your folder. 2. Cut along the dotted height and move the shaded triangle like shown. 3. What special type of parallelogram does the parallelogram now look like? 4. What is the formula for the area of that special type of parallelogram? (Use “b” for base and “h” for height in your formula.) A = 5. Could that same formula be used for the parallelogram? Why or why not? 6. So, what can you conclude is the formula for the area of a parallelogram? Station Two: Area of Triangles Recall that a triangle has three sides. Any side of the triangle can be considered the base (b). In this triangle, we will consider the “bottom” side the base. Any side, however, cannot be the height (h). The height must be perpendicular to the base. It is the distance from a base to the opposite vertex. 1. Locate the two triangles in your folder. 2. Connect the two triangles like shown. 3. What special type of quadrilateral was formed with the two triangles? 4. We know the formula for the area of that special type of quadrilateral is….? A = 5. So, the formula for the area of the two triangles is…? A = 6. So, the formula for the area of one triangle is…? Why? A = Station Three: Area of Trapezoids Recall that a trapezoid is a quadrilateral with only one pair of parallel sides. The lengths of the parallel sides are the bases (b1 and b2). The perpendicular distance between the parallel sides is the height (h) of the trapezoid. 1. Locate the two trapezoids in your folder. 2. Connect the two trapezoids like shown. 3. What special type of quadrilateral was formed with the two trapezoids? 4. Using b and h, what is the formula for the area of that special type of quadrilateral? A = 5. Keeping this in mind, what is the formula for the area of the two trapezoids? (Think about the “base” as a sum of b1 and b2) A = 6. So, what would be the formula for the area of one trapezoid? Why? A = Station Four: Area of Rhombi and Kites Recall that a rhombus is an equilateral quadrilateral and a kite has adjacent congruent sides. Both of these quadrilaterals have perpendicular diagonals, which is how we are going to find their areas. Rhombus Kite 1. Locate the rhombus and kite in your folder. 2. Notice that the diagonals divide each quadrilateral into 4 triangles. In the rhombus, all 4 triangles are congruent, and in the kite there are two sets of congruent triangles. Make a guess: If we rotated the two bottom triangles of each quadrilateral so that they connected with the top triangles above the horizontal diagonal, we would make two ___________________. Rhombus Kite 3. In both the rhombus and kite, cut out the two bottom triangles, rotate them, and connect them to the top triangles to test your theory. 4. So, the height of these ______________ is half of one of the ____________ and the base is the length of the other ______________. 5. So, the formula for the area of each rectangle is…? A = 6. So, the formula for the area of a rhombus and kite is…? A =