Area and Perimeter of Triangles Assignment and Quiz

Jace ordered a banner in the shape of a parallelogram from a print shop. The print shop charges $1.10 per square foot for banners of any shape and size. What is the approximate cost of the banner before tax?

$92.30

The perimeter of triangle XYZ is 24 units. Trigonometric area formula: Area = What is the area of triangle XYZ? Round to the nearest tenth of a square unit.

14.7

Using Heron's formula, calculate the area of the parallelogram to the nearest tenth of a square unit.

36.7 square units

Marta is making a flag with the given dimensions. The perimeter of the flag is 100 inches. How much material, in square inches, is needed to make the flag? If the material costs $0.15 per square inch, how much will Marta spend on materials to make the flag?

360 square inches $54

What is the area of an equilateral triangle that has a perimeter of 36 centimeters? Round to the nearest square centimeter.

62 square centimeters

An equilateral triangle has a semiperimeter of 6 meters. What is the area of the triangle? Round to the nearest square meter.

7 square meters

The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters. If the metal used to construct the spinner costs $13.25 per square centimeter, how much will it cost to make this part of the compass? Round to the nearest cent.

$129.82

The triangle shown is an equilateral triangle. What is the area of the equilateral triangle with the length of each side equal to a?

1/2a^2sin(60°)

What information relevant to calculating area do we have available for this triangle? Which method should we use to calculate the area for this triangle? What is the area of this triangle calculated to the nearest hundredth of a square unit?

SSS Heron's formula 34.98 square units

Consider the diagram and the derivation below. Given: In △ABC, AD ⊥ BC Derive a formula for the area of △ABC using angle C. It is given that in △ABC, AD ⊥ BC. Using the definition of sine with angle C in △ACD results in sin(C) = h/b. Using the multiplication property of equality to isolate h, the equation becomes bsin(C) = h. Knowing that the formula for the area of a triangle is A =1/2bh is and using the side lengths as shown in the diagram, which expression represents the area of △ABC?

1/2absin(C)

Triangle ABC is an equilateral triangle with side lengths labeled a, b, and c. Which expressions represent the area of triangle ABC? Check all that apply.

1/2bcsin(60°) 1/2a^2sin(60°)

What is the area of triangle DEF? Round to the nearest tenth of a square unit.

10.3 square units

What is the area of ΔABC? Round to the nearest tenth of a square unit.

8.4 square units

What is the area of triangle ABC? Round to the nearest hundredth of a square unit.

81.33 square units

Which triangle's area would be calculated using the trigonometric area formula?

B

See the figure of ΔABC with auxiliary lines added. If c is the base of ΔABC, the height is _____, sin(A) = ___ The previous statement is leading to the derivation of which area formula? Area ΔABC =

CD CD/b 1/2bcsin(A)

Which triangle's area can be calculated using the trigonometric area formula?

D

Which statement about the relative areas of ΔABC and ΔXYZ is true?

The area of ΔABC > the area of ΔXYZ