Name: ________________________ Class: ___________________ Date: __________ ID: A Area of Triangles Problem Set Short Answer 1. Two sides of a parallelogram are 24 feet and 30 feet. The measure of the angle between these sides is 57°. Find the area of the parallelogram, to the nearest square foot. - 4. Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his garden will be 55 square yards, find, to the nearest tenth of a degree, the three angles of the triangle. - 2. The two sides and included angle of a parallelogram are 18, 22, and 60°. Find its exact area in simplest form. - 5. A farmer has determined that a crop of strawberries yields a yearly profit of $1.50 per square yard. If strawberries are planted on a triangular piece of land whose sides are 50 yards, 75 yards, and 100 yards, how much profit, to the nearest hundred dollars, would the farmer expect to make from this piece of land during the next harvest? - 3. A ranch in the Australian Outback is shaped like triangle ACE, with m∠A = 42, m∠E = 103 , and AC = 15 miles. Find the area of the ranch, to the nearest square mile. - 6. The triangular top of a table has two sides of 14 inches and 16 inches, and the angle between the sides is 30°. Find the area of the tabletop, in square inches. - 1 Name: ________________________ ID: A 9. In the accompanying diagram of parallelogram ABCD, m∠A = 30, AB = 10, and AD = 6. What is the area of parallelogram ABCD? 7. A triangular plot of land has sides that measure 5 meters, 7 meters, and 10 meters. What is the area of this plot of land, to the nearest tenth of a square meter? - 8. The accompanying diagram shows a triangular plot of land that is part of Fran's garden. She needs to change the dimensions of this part of the garden, but she wants the area to stay the same. She increases the length of side AC to 22.5 feet. If angle A remains the same, by how many feet should side AB be decreased to make the area of the new triangular plot of land the same as the current one? 10. The accompanying diagram shows a triangular plot of land located in Moira’s garden. Find the area of the plot of land, and round your answer to the nearest hundred square feet. 2 ID: A Area of Triangles Problem Set Answer Section SHORT ANSWER 1. ANS: K = absinC = 24 ⋅ 30sin57 ≈ 604 PTS: 2 REF: 061034a2 KEY: parallelograms 2. ANS: K = absinC = 18 ⋅ 22sin60 = 396 STA: A2.A.74 TOP: Using Trigonometry to Find Area 3 = 198 3 2 PTS: 2 REF: 061234a2 KEY: Parallelograms 3. ANS: 1 a 15 = . (15)(10.3) sin35 ≈ 44 sin103 sin 42 2 STA: A2.A.74 TOP: Using Trigonometry to Find Area REF: 061337a2 STA: A2.A.74 TOP: Using Trigonometry to Find Area REF: 060121b STA: A2.A.74 TOP: Using Trigonometry to Find Area a ≈ 10.3 PTS: 4 KEY: advanced 4. ANS: 49.8°, 65.1°, 65.1°. PTS: 2 KEY: advanced 5. ANS: . 2700. PTS: 6 6. ANS: REF: 060333b STA: A2.A.74 TOP: Heron’s Formula PTS: 2 REF: 080324b KEY: without calculator STA: A2.A.74 TOP: Using Trigonometry to Find Area 56. 1 ID: A 7. ANS: 16.2. PTS: 6 8. ANS: 2. REF: 060634b STA: A2.A.74 TOP: Heron’s Formula Side AB should be decreased from 18 to 16, . or by 2 feet. PTS: 4 KEY: advanced 9. ANS: 30. REF: 080628b STA: A2.A.74 TOP: Using Trigonometry to Find Area PTS: 2 REF: 010924b KEY: parallelograms 10. ANS: STA: A2.A.74 TOP: Using Trigonometry to Find Area STA: A2.A.74 TOP: Heron’s Formula 8,200. PTS: 6 REF: 060933b 2

© Copyright 2018