Triangle/Quad Area

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Answer Key & Explanations

Triangle/Quad Area · Grade 6 · Worksheet 1

1. A triangular garden has a base of 17 m and a height of 13 m. What is its area in square meters? Answer: 110.5 Solution: Write the formula for the area of a triangle: A = 1/2 × base × height. Substitute the given values: base = 17 m, height = 13 m. Multiply base and height: 17 × 13 = 221.
   Full step-by-step solution

   Step 1: Write the formula for the area of a triangle: A = 1/2 × base × height. Step 2: Substitute the given values: base = 17 m, height = 13 m. Step 3: Multiply base and height: 17 × 13 = 221. Step 4: Multiply by 1/2: 221 × 1/2 = 110.5. The area of the triangular garden is 110.5 square meters.

2. A trapezoid has bases of 14 cm and 22 cm, and a height of 9 cm. What is its area in square centimeters? Answer: 162 Solution: Recall 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: Recall 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 the sum 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.

3. Max is helping build a garden shaped like a parallelogram. The base of the garden is 8 feet and the height (perpendicular distance between the bases) is 7 feet. What is the area of the garden in square feet? Answer: 56 Solution: Recall the formula for the area of a parallelogram: Area = base × height. Plug in the values: base = 8 feet, height = 7 feet. Area = 8 × 7.
   Full step-by-step solution

   Step 1: Recall the formula for the area of a parallelogram: Area = base × height. Step 2: Plug in the values: base = 8 feet, height = 7 feet. Step 3: Area = 8 × 7. Step 4: Multiply: 8 × 7 = 56. The area of the garden is 56 square feet.

4. A trapezoid has bases of 15 cm and 9 cm, and a height of 7 cm. What is its area? Answer: 84 Solution: Identify the formula for the area of a trapezoid: A = (1/2) * (base1 + base2) * height. Substitute the given values: base1 = 15 cm, base2 = 9 cm, height = 7 cm. Add the bases: 15 + 9 = 24.
   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 = 9 cm, height = 7 cm. Step 3: Add the bases: 15 + 9 = 24. Step 4: Multiply the sum by the height: 24 * 7 = 168. Step 5: Multiply by 1/2: 168 * 1/2 = 84. The area of the trapezoid is 84 square centimeters.

5. Liam is designing a triangular garden with a base of 12 meters and a height of 8 meters. He also wants to build a rectangular patio next to it that is 10 meters long and 7 meters wide. What is the total area, in square meters, that Liam's garden and patio will cover? Answer: 118 Solution: Area = (1/2) × base × height Here, base = 12 m, height = 8 m. Area of triangle = (1/2) × 12 × 8 = (1/2) × 96 = 48 square meters Area = length × width Here, length = 10 m, width = 7 m.
   Full step-by-step solution

   Let's find the total area step by step. --- **Step 1: Find the area of the triangular garden** The formula for the area of a triangle is: Area = (1/2) × base × height Here, base = 12 m, height = 8 m. Area of triangle = (1/2) × 12 × 8 = (1/2) × 96 = 48 square meters --- **Step 2: Find the area of the rectangular patio** The formula for the area of a rectangle is: Area = length × width Here, length = 10 m, width = 7 m. Area of rectangle = 10 × 7 = 70 square meters --- **Step 3: Add the two areas together** Total area = Area of triangle + Area of rectangle = 48 + 70 = 118 square meters --- **Final Answer:** 118

6. √(144) + 3² - 5 × 2 = ? Answer: 11 Solution: √(144) + 3² - 5 × 2 Handle exponents and square roots first (order of operations: PEMDAS/BODMAS). √(144) = 12, because 12 × 12 = 144. 3² = 3 × 3 = 9.
   Full step-by-step solution

   Let's solve step-by-step: Step 1: Identify the operations in the expression: √(144) + 3² - 5 × 2 Step 2: Handle exponents and square roots first (order of operations: PEMDAS/BODMAS). √(144) = 12, because 12 × 12 = 144. 3² = 3 × 3 = 9. So now we have: 12 + 9 - 5 × 2 Step 3: Handle multiplication before addition and subtraction. 5 × 2 = 10. Now we have: 12 + 9 - 10 Step 4: Perform addition and subtraction from left to right. 12 + 9 = 21 21 - 10 = 11 Final answer: 11

7. A rectangular garden has a length of 12.5 meters and a width that is 60% of the length. A triangular flower bed is built inside the garden with its base equal to the garden's width and its height equal to 80% of the garden's length. What is the area of the triangular flower bed in square meters? Answer: 37.5 Solution: Find the width of the rectangular garden. The length is given as 12.5 meters. The width is 60% of the length.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the width of the rectangular garden.** The length is given as 12.5 meters. The width is 60% of the length. Width = 60% of 12.5 = (60/100) × 12.5 = 0.6 × 12.5 = 7.5 meters. So, width = 7.5 m. --- **Step 2: Identify the base and height of the triangular flower bed.** The problem says: - Base of triangle = garden's width = 7.5 m - Height of triangle = 80% of garden's length Height = 80% of 12.5 = (80/100) × 12.5 = 0.8 × 12.5 = 10 meters. So, base = 7.5 m, height = 10 m. --- **Step 3: Calculate the area of the triangle.** Area of a triangle = (1/2) × base × height Area = (1/2) × 7.5 × 10 = 0.5 × 7.5 × 10 = 0.5 × 75 = 37.5 square meters. --- **Final answer:** 37.5