Developing Formulas 10 1 Triangles andand Quadrilaterals Triangles

10 -1 Developing Formulas Triangles and Quadrilaterals Warm Up Find the unknown side length

10 -1 Developing Formulas Triangles and Quadrilaterals Objectives Develop and apply the formulas for

10 -1 Developing Formulas Triangles and Quadrilaterals A rectangle with base b and height

10 -1 Developing Formulas Triangles and Quadrilaterals Remember that rectangles and squares are also

10 -1 Developing Formulas Triangles and Quadrilaterals Remember! The height of a parallelogram is

10 -1 Developing Formulas Triangles and Quadrilaterals Remember! The perimeter is the sum of

10 -1 Developing Formulas Triangles and Quadrilaterals Example 1 A: Finding Measurements of Parallelograms

10 -1 Developing Formulas Triangles and Quadrilaterals Check It Out! Example 1 Find the

10 -1 Developing Formulas Triangles and Quadrilaterals Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Example 2 A: Finding Measurements of Triangles

10 -1 Developing Formulas Triangles and Quadrilaterals Example 2 C: Finding Measurements of Triangles

10 -1 Developing Formulas Triangles and Quadrilaterals Check It Out! Example 2 Find the

10 -1 Developing Formulas Triangles and Quadrilaterals Remember! The diagonals of a rhombus or

10 -1 Developing Formulas Triangles and Quadrilaterals Example 3 A: Finding Measurements of Rhombuses

10 -1 Developing Formulas Triangles and Quadrilaterals Example 3 C: Finding Measurements of Rhombuses

10 -1 Developing Formulas Triangles and Quadrilaterals Example 3 C Continued Step 2 Use

10 -1 Developing Formulas Triangles and Quadrilaterals Homework/Classwork: • 10. 1 #’s: 1, 4,

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Developing Formulas 10 -1 Triangles andand Quadrilaterals Triangles Quadrilaterals Warm Up Lesson Presentation Lesson Quiz Holt. Mc. Dougal Geometry Holt

10 -1 Developing Formulas Triangles and Quadrilaterals Warm Up Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = 21 2. b = 21, c = 35 c = 29 a = 28 3. a = 20, c = 52 b = 48 Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Objectives Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles and special quadrilaterals. Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals A rectangle with base b and height h has an area of A = bh. A parallelogram has the same area as a rectangle with the same base and height. Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Remember that rectangles and squares are also parallelograms. Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Remember! The height of a parallelogram is measured along a segment perpendicular to a line containing the base. Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Remember! The perimeter is the sum of all the sides. Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Example 1 A: Finding Measurements of Parallelograms Find the area of the parallelogram. Step 1 Use the Pythagorean Theorem to find the height h. 302 + h 2 = 342 h = 16 Step 2 Use h to find the area of the parallelogram. A = bh Area of a parallelogram A = 11(16) Substitute 11 for b and 16 for h. A = 176 mm 2 Simplify. Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Check It Out! Example 1 Find the base of the parallelogram in which h = 56 yd and A = 28 yd 2. A = bh 28 = b(56) 56 56 b = 0. 5 yd Holt Mc. Dougal Geometry Area of a parallelogram Substitute. Simplify.

10 -1 Developing Formulas Triangles and Quadrilaterals Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Example 2 A: Finding Measurements of Triangles and Trapezoids Find the area of a trapezoid in which b 1 = 8 in. , b 2 = 5 in. , and h = 6. 2 in. Area of a trapezoid Substitute 8 for b 1, 5 for b 2, and 6. 2 for h. A = 40. 3 in 2 Holt Mc. Dougal Geometry Simplify.

10 -1 Developing Formulas Triangles and Quadrilaterals Example 2 C: Finding Measurements of Triangles and Trapezoids Find b 2 of the trapezoid, in which A = 231 mm 2. Area of a trapezoid Substitute 231 for A, 23 for and 11 for h. 42 = 23 + b 2 Multiply both sides by 19 = b 2 Subtract 23 from both sides. b 2 = 19 mm Sym. Prop. of = Holt Mc. Dougal Geometry . ,

10 -1 Developing Formulas Triangles and Quadrilaterals Check It Out! Example 2 Find the area of the triangle. Find b. Area of a triangle Substitute 16 for b and 12 for h. A = 96 m 2 Holt Mc. Dougal Geometry Simplify.

10 -1 Developing Formulas Triangles and Quadrilaterals Remember! The diagonals of a rhombus or kite are perpendicular, and the diagonals of a rhombus bisect each other. Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Example 3 A: Finding Measurements of Rhombuses and Kites Find d 2 of a kite in which d 1 = 14 in. and A = 238 in 2. Area of a kite Substitute 238 for A and 14 for d 1. 34 = d 2 Solve for d 2 = 34 Sym. Prop. of = Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Example 3 C: Finding Measurements of Rhombuses and Kites Find the area of the kite Step 1 The diagonals d 1 and d 2 form four right triangles. Use the Pythagorean Theorem to find x and y. 282 + y 2 = 352 212 + x 2 = 292 y 2 = 441 x 2 = 400 y = 21 x = 20 Holt Mc. Dougal Geometry

10 -1 Developing Formulas Triangles and Quadrilaterals Example 3 C Continued Step 2 Use d 1 and d 2 to find the area. d 1 is equal to x + 28, which is 48. Half of d 2 is equal to 21, so d 2 is equal to 42. Area of kite Substitute 48 for d 1 and 42 for d 2. A = 1008 in 2 Holt Mc. Dougal Geometry Simplify.

10 -1 Developing Formulas Triangles and Quadrilaterals Homework/Classwork: • 10. 1 #’s: 1, 4, 5, 7, 8, 11, 14, 15, 23, 24, 25 Holt Mc. Dougal Geometry