Triangle/Quad Area

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Triangle/Quad Area · Grade 6 · Worksheet 3

1. Ava is designing a parallelogram-shaped garden. The base of the garden is 5 meters and the height (the perpendicular distance between the bases) is 17 meters. How many square meters of grass seed will Ava need to cover the entire garden? Answer: 85 Solution: Recall the formula for the area of a parallelogram: Area = base × height. Substitute the base = 5 meters and height = 17 meters: Area = 5 × 17. Multiply: 5 × 17 = 85.
   Full step-by-step solution

   Step 1: Recall the formula for the area of a parallelogram: Area = base × height. Step 2: Substitute the base = 5 meters and height = 17 meters: Area = 5 × 17. Step 3: Multiply: 5 × 17 = 85. Ava will need 85 square meters of grass seed.

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. A triangle has a base of 16 cm and a height of 11 cm. A parallelogram has a base of 16 cm and a height of 11 cm. What is the total area of both shapes in square centimeters? Answer: 264 Solution: Find the area of the triangle. Area = 1/2 × base × height = 1/2 × 16 × 11 = 1/2 × 176 = 88 square cm. Find the area of the parallelogram.
   Full step-by-step solution

   Step 1: Find the area of the triangle. Area = 1/2 × base × height = 1/2 × 16 × 11 = 1/2 × 176 = 88 square cm. Step 2: Find the area of the parallelogram. Area = base × height = 16 × 11 = 176 square cm. Step 3: Add the two areas together: 88 + 176 = 264 square cm. The answer is 264.

4. 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.

5. A rectangular garden has a length of 12.5 m and a width of 8.4 m. What is its area in square meters? Answer: 105 Solution: To find the area of a rectangle, we use the formula: Area = length × width Write down the given measurements. Length = 12.5 m Width = 8.4 m Substitute the values into the formula. Area = 12.5 × 8.4 Multiply the numbers.
   Full step-by-step solution

   To find the area of a rectangle, we use the formula: Area = length × width Step 1: Write down the given measurements. Length = 12.5 m Width = 8.4 m Step 2: Substitute the values into the formula. Area = 12.5 × 8.4 Step 3: Multiply the numbers. First, ignore the decimal points and multiply 125 by 84. 125 × 84 = ? 125 × 80 = 10,000 125 × 4 = 500 10,000 + 500 = 10,500 Step 4: Now, account for the decimals. In the original numbers, 12.5 has one digit after the decimal, and 8.4 also has one digit after the decimal. This is a total of two decimal places. So, we take our result of 10,500 and put the decimal point two places from the right. 10,500 becomes 105.00 Step 5: Write the final answer with the correct units. Area = 105 square meters Therefore, the area of the garden is 105 square meters.

6. A trapezoid has bases of 18 cm and 12 cm, and a height of 14 cm. What is its area in square centimeters? Answer: 210 Solution: Identify the formula for the area of a trapezoid: A = (1/2) * (base1 + base2) * height. Substitute the given values: base1 = 18 cm, base2 = 12 cm, height = 14 cm. Add the bases: 18 + 12 = 30.
   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 = 18 cm, base2 = 12 cm, height = 14 cm. Step 3: Add the bases: 18 + 12 = 30. Step 4: Multiply by the height: 30 * 14 = 420. Step 5: Multiply by 1/2: (1/2) * 420 = 210. The area of the trapezoid is 210 square centimeters.

7. Liam is designing a parallelogram-shaped garden. The base of the garden is 15 meters and the height (the perpendicular distance between the bases) is 4 meters. How many square meters of grass seed will Liam need to cover the entire garden? Answer: 60 Solution: Recall the formula for the area of a parallelogram: Area = base × height. Substitute the base = 15 meters and height = 4 meters: Area = 15 × 4. Multiply: 15 × 4 = 60.
   Full step-by-step solution

   Step 1: Recall the formula for the area of a parallelogram: Area = base × height. Step 2: Substitute the base = 15 meters and height = 4 meters: Area = 15 × 4. Step 3: Multiply: 15 × 4 = 60. Liam will need 60 square meters of grass seed.