Math Area of Parallelograms 9.3 Notes

LESSON 9-3: Area of Parallelograms The area of a figure is the number of square units inside the figure. You can count the squares inside the rectangle. There are 15 square units within the rectangle. This is equal to 5 1 x 3. To find the area of a rectangle, multiply the length (l) by the width (w). A = l * w Find the area of each rectangle. A = l * w A = 7 * 9 A = 63 yd² The area is 63 yd². A = l * w A = 12 * 5 A = 60 in² The area is 60 in². To find the area of a parallelogram, multiply the base (b) times the height (h). A = b * h Find the area of each parallelogram. A = b * h A = 4 * 8 A = 32 yd² The area is 32 yd². A = b * h A = 9 * 6 A = 54 cm² The area is 54 cm². LESSON 9-4: Area of Triangles and Trapezoids The diagram shows how you can cut a parallelogram into two congruent triangles. Remember that the formula for the area of a parallelogram is A = b * h. The area of the triangle is 1/2 the area of the parallelogram. The formula for the area of a triangle is A = (1/2) * b * h. Find the area of each triangle. A = (1/2) * b * h A = (1/2) * 5 * 2 A = 5 units² The area of the triangle is 5 units². A = (1/2) * b * h A = (1/2) * 9 * 8 A = 36 units² The area of the triangle is 36 units². A = (1/2) * b * h A = (1/2) * 7 * 6 A = 21 in² A = (1/2) * b * h A = (1/2) * 3 * 7 A = 10.5 cm² A = (1/2) * b * h A = (1/2) * 9 * 4 A = 18 yd² What is the area of a triangle with base 16 m and height 10 m? A = (1/2) * 16 * 10 = 80 m² What is the area of a triangle with base 25 mm and height 50 mm? A = (1/2) * 25 * 50 = 625 mm² LESSON 9-4: Area of Triangles and Trapezoids (Continued) In a trapezoid, the parallel sides are called the bases. One base is always longer than the other. The bases are labeled base 1 and base 2. Area of trapezoid = 1/2 * h * (b₁ + b₂) Find the area of each trapezoid. A = 1/2 * h * (b₁ + b₂) A = 1/2 * 4 * (7 + 3) A = 1/2 * 4 * 10 A = 20 in² The area of the trapezoid is 20 in². A = 1/2 * h * (b₁ + b₂) A = 1/2 * 5 * (8 + 6) A = 1/2 * 5 * 14 A = 35 cm² The area of the trapezoid is 35 cm². A = 1/2 * h * (b₁ + b₂) A = 1/2 * 6 * (9 + 5) A = 1/2 * 6 * 14 A = 42 ft² The area of the trapezoid is 42 ft². A = 1/2 * h * (b₁ + b₂) A = 1/2 * 4 * (8 + 4) A = 1/2 * 4 * 12 A = 24 m² The area of the trapezoid is 24 m². A = 1/2 * h * (b₁ + b₂) A = 1/2 * 4 * (7 + 3) A = 1/2 * 4 * 10 A = 20 cm² The area of the trapezoid is 20 cm². What is the area of a trapezoid with bases 25 yd and 75 yd and height 10 yd? A = 1/2 * h * (b₁ + b₂) A = 1/2 * 10 * (25 + 75) A = 5 * 100 A = 500 yd² LESSON 9-4: Area of Triangles and Trapezoids Find the area of each triangle. A = (1/2) * b * h A = (1/2) * 7 * 6 A = 21 units² The area of the triangle is 21 units². A = (1/2) * b * h A = (1/2) * 9 * 4 A = 18 units² The area of the triangle is 18 units². A = (1/2) * b * h A = (1/2) * 13 * 5 A = 32.5 units² The area of the triangle is 32.5 units². Find the area of each rectangle. A = l * w A = 12.5 * 5 A = 62.5 cm² The area of the rectangle is 62.5 cm². A = l * w A = 6 * 6 A = 36 cm² The area of the rectangle is 36 cm². A = l * w A = 10 * 4.8 A = 48 cm² The area of the rectangle is 48 cm². Find the area of each parallelogram. A = b * h A = 9 * 8 A = 72 cm² The area of the parallelogram is 72 cm². A = b * h A = 7 * 2 A = 14 cm² The area of the parallelogram is 14 cm². 9. Michelle wants to carpet her living room. The area of the living room is 192 ft². The length of the living room is 16 ft. What is the width of the living room? Area = Length × Width 192 = 16 × Width Width = 192 / 16 Width = 12 ft 10. Mustafa is tiling his bathroom. The section that needs to be tiled is 62 in. by 70 in. How many square inches of tile does he need? Area = Length × Width Area = 62 in × 70 in Area = 4340 in²