Triangle/Quad Area

lessonbunny.com

Answer Key & Explanations

Triangle/Quad Area · Grade 6 · Worksheet 3

1. Kai is building a kite in the shape of a parallelogram. The base of the kite measures 28 inches and the vertical height (the perpendicular distance between the top and bottom edges) measures 15 inches. How much fabric, in square inches, does Kai need to cover the kite? Answer: 420 Solution: The formula for the area of a parallelogram is A = base × height. Substitute the values: A = 28 × 15 Multiply: 28 × 15 = 420 The answer is 420 square inches.
   Full step-by-step solution

   Step 1: The formula for the area of a parallelogram is A = base × height. Step 2: Substitute the values: A = 28 × 15 Step 3: Multiply: 28 × 15 = 420 The answer is 420 square inches.

2. Liam is designing a triangular garden with a base of 12 meters and a height of 8 meters. He also wants to add a rectangular flower bed that is 5 meters long and 3 meters wide. What is the total area, in square meters, that Liam will use for his garden and flower bed combined? Answer: 63 Solution: Find the area of the triangular garden. Area = (base × height) / 2 Given: base = 12 m, height = 8 m Area of triangle = (12 × 8) / 2 = 96 / 2 = 48 square meters Find the area of the rectangular flower bed.
   Full step-by-step solution

   Step 1: Find the area of the triangular garden. The formula for the area of a triangle is: Area = (base × height) / 2 Given: base = 12 m, height = 8 m Area of triangle = (12 × 8) / 2 = 96 / 2 = 48 square meters Step 2: Find the area of the rectangular flower bed. The formula for the area of a rectangle is: Area = length × width Given: length = 5 m, width = 3 m Area of rectangle = 5 × 3 = 15 square meters Step 3: Add the two areas to get the total area. Total area = area of triangle + area of rectangle = 48 + 15 = 63 square meters Final answer: 63

3. Leo is building a kite in the shape of a parallelogram. The base of the kite measures 29 inches and the vertical height (the perpendicular distance between the top and bottom edges) measures 10 inches. How much fabric, in square inches, does Leo need to cover the kite? Answer: 290 Solution: The formula for the area of a parallelogram is A = base × height. Substitute the values: A = 29 × 10 Multiply: 29 × 10 = 290 The answer is 290 square inches.
   Full step-by-step solution

   Step 1: The formula for the area of a parallelogram is A = base × height. Step 2: Substitute the values: A = 29 × 10 Step 3: Multiply: 29 × 10 = 290 The answer is 290 square inches.

4. A rectangular garden measures 12.5 meters by 8.4 meters. A triangular flower bed is built inside it, with its base along the entire 12.5-meter side and its apex touching the opposite side. What is the area of the garden that is NOT covered by the flower bed? Answer: 52.5 Solution: - Length = 12.5 m - Width = 8.4 m - Base = entire 12.5 m side - Apex touching the opposite side (so height of triangle = width of rectangle = 8.4 m) We need the area not covered by the flower bed.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** We have a rectangular garden with: - Length = 12.5 m - Width = 8.4 m A triangular flower bed is built with: - Base = entire 12.5 m side - Apex touching the opposite side (so height of triangle = width of rectangle = 8.4 m) We need the area **not** covered by the flower bed. --- **Step 2: Find the area of the rectangle** Area of rectangle = length × width = 12.5 × 8.4 Calculate: 12.5 × 8 = 100 12.5 × 0.4 = 5 So 100 + 5 = 105 Area of rectangle = 105 m² --- **Step 3: Find the area of the triangular flower bed** Area of triangle = (1/2) × base × height = (1/2) × 12.5 × 8.4 First, 12.5 × 8.4 = 105 (we already computed above) Then multiply by 1/2: 105 × 1/2 = 52.5 Area of triangle = 52.5 m² --- **Step 4: Find the area not covered by the flower bed** Area not covered = Area of rectangle − Area of triangle = 105 − 52.5 = 52.5 m² --- **Step 5: Conclusion** The area of the garden not covered by the flower bed is 52.5 m². --- **Final answer:** 52.5

5. A trapezoid has bases of 14 cm and 22 cm, and a height of 9 cm. What is its area? Answer: 162 Solution: Identify the formula for the area of a trapezoid: A = 1/2 × (base1 + base2) × height. Substitute the given values: base1 = 14 cm, base2 = 22 cm, height = 9 cm. Add the bases: 14 + 22 = 36.
   Full step-by-step solution

   Step 1: Identify the formula for the area of a trapezoid: A = 1/2 × (base1 + base2) × height. Step 2: Substitute the given values: base1 = 14 cm, base2 = 22 cm, height = 9 cm. Step 3: Add the bases: 14 + 22 = 36. Step 4: Multiply by the height: 36 × 9 = 324. Step 5: Multiply by 1/2: 324 × 1/2 = 162. The area of the trapezoid is 162 square centimeters.

6. A trapezoid has bases of 15 cm and 25 cm, and a height of 10 cm. What is its area? Answer: 200 Solution: Identify the formula for the area of a trapezoid: A = 1/2 × (base1 + base2) × height. Substitute the given values: base1 = 15 cm, base2 = 25 cm, height = 10 cm. Add the bases: 15 + 25 = 40.
   Full step-by-step solution

   Step 1: Identify the formula for the area of a trapezoid: A = 1/2 × (base1 + base2) × height. Step 2: Substitute the given values: base1 = 15 cm, base2 = 25 cm, height = 10 cm. Step 3: Add the bases: 15 + 25 = 40. Step 4: Multiply the sum by the height: 40 × 10 = 400. Step 5: Multiply by 1/2: 1/2 × 400 = 200. The area of the trapezoid is 200 square centimeters.