Download G.SRT.D.9 Assessment Items

Item #1
Find the area of an equilateral triangle in which the length of each side is 18 inches. Find
your answer in two ways.
a. Use the traditional area formula by first finding the height of the triangle.
b. Use the trigonometric area formula for a triangle.
c. Give examples of cases in which you would use the formula A = ½ bh versus using the
formula A = ½ ab sinC.
Solution:
a. 140.296 inches2
b. 140.296 inches2
c. Solutions may vary. One example for using the trigonometric area formula: The adjacent
sides and the included angle are given. In other instances, one would use the A = ½ bh formula
and trigonometric ratios to find the missing parts needed to derive the area.
Item #2
David wants to add mulch to his triangular garden in his backyard. He uses a yard stick to
measure the adjacent sides. The sides are 15 feet and 24 feet. He measures, with a protractor,
the included angle to be 78°.
a. How much area needs to be covered with mulch?
b. A bag of mulch covers approximately 36 square feet if it is poured out to be one inch high.
How many bags of mulch would be needed to cover the area of the garden?
Solution:
a. A = ½ (15)(24)(sin78°) ≈ 176 square feet
b. 4.89 bags