Areas of Triangles and Parallelograms. Bases of a parallelogram. Height of a parallelogram THEOREM 11.3: AREA OF A TRIANGLE. a and its corresponding.
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1 11.1 Areas of Triangles and Parallelograms Goal p Find areas of triangles and parallelograms. Your Notes VOCABULARY Bases of a parallelogram Heigt of a parallelogram POSTULATE 4: AREA OF A SQUARE POSTULATE Te area of a square is te of te lengt of its side. POSTULATE 5: AREA CONGRUENCE POSTULATE If two polygons are, ten tey ave te same area. POSTULATE 6: AREA ADDITION POSTULATE Te area of a region is te of te areas of its nonoverlapping parts. THEOREM 11.1: AREA OF A RECTANGLE Te area of a rectangle is te product of its and. THEOREM 11.: AREA OF A PARALLELOGRAM Te area of a parallelogram is te product of a and its corresponding. THEOREM 11.3: AREA OF A TRIANGLE Te area of a triangle is te product of a and its corresponding. Copyrigt Holt McDougal. All rigts reserved. Lesson 11.1 Geometry Notetaking Guide 95
2 11.1 Areas of Triangles and Parallelograms Goal p Find areas of triangles and parallelograms. Your Notes VOCABULARY Bases of a parallelogram Eiter pair of parallel sides of a parallelogram are bases. Heigt of a parallelogram Te sortest distance between bases of a parallelogram is te eigt. POSTULATE 4: AREA OF A SQUARE POSTULATE Te area of a square is te square of te lengt of its side. POSTULATE 5: AREA CONGRUENCE POSTULATE If two polygons are congruent, ten tey ave te same area. POSTULATE 6: AREA ADDITION POSTULATE Te area of a region is te sum of te areas of its nonoverlapping parts. THEOREM 11.1: AREA OF A RECTANGLE Te area of a rectangle is te product of its base and eigt. THEOREM 11.: AREA OF A PARALLELOGRAM Te area of a parallelogram is te product of a base and its corresponding eigt. THEOREM 11.3: AREA OF A TRIANGLE Te area of a triangle is one alf te product of a base and its corresponding eigt. Copyrigt Holt McDougal. All rigts reserved. Lesson 11.1 Geometry Notetaking Guide 95
3 Example 1 Find te area of ~ABCD. Use a formula to find area 4.5 E A 9 D Metod 1 Use } AD as te base. Te base is extended to measure te eigt. So, b 5 and 5. Area 5 b 5 ( ) 5 square units Metod Use } AB as te base. Ten te eigt is. So, b 5 and 5. Area 5 b 5 ( ) 5 square units 8 B C F 4 Ceckpoint Find te area of te polygon Example Solve for unknown measures Te base of a triangle is four times its eigt. Te area of te triangle is 50 square inces. Find te base and eigt. Note tat tere are oter ways you can draw te triangle in Example. Let represent te eigt of te triangle. Ten te base is. A 5 } 1 b Write formula. 5 } 1 ( )() Substitute for A and for b. 5 Simplify. 5 Divide eac side by. 5 Find positive square root of eac side. Te eigt of te triangle is inces, and te base is 4 p 5 inces. 96 Lesson 11.1 Geometry Notetaking Guide Copyrigt Holt McDougal. All rigts reserved.
4 Example 1 Find te area of ~ABCD. Use a formula to find area 4.5 E A 9 D Metod 1 Use } AD as te base. Te base is extended to measure te eigt CF. So, b 5 9 and 5 4. Area 5 b 5 9 ( 4 ) 5 36 square units Metod Use } AB as te base. Ten te eigt is BE. So, b 5 8 and Area 5 b 5 8 ( 4.5 ) 5 36 square units 8 B C F 4 Ceckpoint Find te area of te polygon square units 119 square units Example Solve for unknown measures Te base of a triangle is four times its eigt. Te area of te triangle is 50 square inces. Find te base and eigt. Note tat tere are oter ways you can draw te triangle in Example. Let represent te eigt of te triangle. Ten te base is. A 5 } 1 b Write formula } 1 ( )() Substitute 50 for A and for b Simplify. 5 5 Divide eac side by. 5 5 Find positive square root of eac side. Te eigt of te triangle is 5 inces, and te base is 4 p inces. 96 Lesson 11.1 Geometry Notetaking Guide Copyrigt Holt McDougal. All rigts reserved.
5 Example 3 Solve a multi-step problem Vacuum A robotic vacuum cleaner can clean square meters of carpet in 8 minutes. About ow long does it take for it to clean a carpet covering a room wit te dimensions sown at te rigt? Step 1 Find te area of te carpet. Area 5 Area of rectangle 1 Area of square 5 4( ) 1 5( ) Step Determine ow long it takes te robotic vacuum to clean te carpet. m p min inutes Use unit m analysis. It takes minutes, or about ours for te robotic vacuum to clean te carpet. Ceckpoint Complete te following exercises. 3. A parallelogram as an area of 133 square feet and a eigt of 19 feet. Wat is te lengt of te base? Homework 4. In Example 3, suppose tere are 4 sections of carpet measuring 1 meter by meters tat are covered and cannot be cleaned. About ow many ours does it take for te robotic vacuum to clean te carpet? Copyrigt Holt McDougal. All rigts reserved. Lesson 11.1 Geometry Notetaking Guide 97
6 Example 3 Solve a multi-step problem Vacuum A robotic vacuum cleaner can clean square meters of carpet in 8 minutes. About ow long does it take for it to clean a carpet covering a room wit te dimensions sown at te rigt? Step 1 Find te area of te carpet. Area 5 Area of rectangle 1 Area of square 5 4( 9 ) 1 5( 5 ) 5 61 m Step Determine ow long it takes te robotic vacuum to clean te carpet. 61 m p 8 min 5 44 minutes Use unit m analysis. It takes 44 minutes, or about 4 ours for te robotic vacuum to clean te carpet. Ceckpoint Complete te following exercises. 3. A parallelogram as an area of 133 square feet and a eigt of 19 feet. Wat is te lengt of te base? 7 feet Homework 4. In Example 3, suppose tere are 4 sections of carpet measuring 1 meter by meters tat are covered and cannot be cleaned. About ow many ours does it take for te robotic vacuum to clean te carpet? about 3.5 ours Copyrigt Holt McDougal. All rigts reserved. Lesson 11.1 Geometry Notetaking Guide 97
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