1. Daily Warm-UP Quiz 1.Write the distance formula: d = ___________________ 2. Write the slope formula: 3. Given: A (-5,2) B (-3,6) Find a. The slope of AB Find b. The length of AB Mrs. McConaughyGeometry1

2. Mrs. McConaughyGeometry2 Lesson 7.1: Areas of Triangles and Quadrilaterals Objective: To find the areas of squares, rectangles, parallelograms, and triangles

3. Mrs. McConaughyGeometry3 AREA POSTULATES AREA OF A SQUARE POSTULATE The area of a square is _____________ ______________________________. AREA CONGRUENCE POSTULATE If two polygons are congruent, _______ ______________________________. AREA ADDITION POSTULATE The area of a region is _____________ ______________________________. A = s 2, where s is the length of its side. then they have the same area. the sum of the areas of its non-overlapping parts.

4. Mrs. McConaughyGeometry4 AREA THEOREMS A = ½ bh * Area = bh Area of a Triangle The area of a parallelogram is one half the product of a base and its corresponding height* (where h is the altitude). Area of a Rectangle (or Square)* The area of a rectangle (or square) is the product of its base and height. Area of a Parallelogram The area of a parallelogram is the product of a base and its corresponding height* (where height is the altitude). Area = bh* NOTE: Area is always measured in square units. b h b h b h

5. Mrs. McConaughyGeometry5 Using Area Theorems: Parallelograms A base of a parallelogram is _______________________________. The height of a parallelogram corresponding to a given base is _______________________________ _______________________________. any of its sides the perpendicular segment to the line containing the base (altitude).

6. Mrs. McConaughyGeometry6 Find the area of ABCD. Area = bh Area = (16) (9) Area = 144 units 2 OR Area = bh Area = (12) (12) Area = 144 units 2 Note: You get the same area with either base. Remember: Area is always measured in square units.

7. Mrs. McConaughyGeometry7 Finding a Missing Dimension Given: Area = 126 cm 2 h = 14 cm b = ___________

8. Mrs. McConaughyGeometry8 Finding a Missing Dimension A parallelogram has sides of 15 cm and 18 cm. The height corresponding to a 15-cm base is 9 cm. Draw the parallelogram and find the height corresponding to an 18-cm base. 15 cm 18 cm 9 cm

9. Mrs. McConaughyGeometry9 Work Space: Area = bh = ______ Area = bh ____ = _____ Remember: Area is always measured in square units.

10. Mrs. McConaughyGeometry10 Using Area Theorems: Triangles A base of a triangle is _____________________________. The height of a triangle is _____________________________ _____________________________. any of its sides the length of the altitude to the line containing that base

11. Mrs. McConaughyGeometry11 Identifying the base and height in triangles.

12. Mrs. McConaughyGeometry12 Using Areas: Triangle Areas Find the area of the TRIANGLE at the left. Area = _________ ½ bh ½ (12m) (15 m) 90 m 2 Remember: Area is always measured in square units.

13. Mrs. McConaughyGeometry13 Structural Design The front of a garage is a square 15 ft. on each side with a triangular roof above the square. The height of the triangular roof is 10.6 ft. To the nearest hundredth, how much force is exerted by an 80 mi/h wind blowing directly against the front of the garage? Use the formula, F = 0.004 Av2, where F is the force in pounds, A is the surface area in square feet, and v is the velocity of the wind in mph.

14. Mrs. McConaughyGeometry14 FINAL CHECKS FOR UNDERSTANDING 1. If you use AB as the base to find the area of parallelogram ABCD shown at the right, what should you use as the height? 2. Find the area of the polygon. HOMEWORK: _______________________