Triangle/Quad Area

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Triangle/Quad Area · Grade 6 · Worksheet 1

1. A trapezoid has bases of 16 cm and 26 cm, and a height of 11 cm. What is its area? Answer: 231 Solution: Identify the bases: base1 = 16 cm, base2 = 26 cm, height = 11 cm. Use the formula for area of a trapezoid: A = (1/2) * (base1 + base2) * height. Add the bases: 16 + 26 = 42.
   Full step-by-step solution

   Step 1: Identify the bases: base1 = 16 cm, base2 = 26 cm, height = 11 cm. Step 2: Use the formula for area of a trapezoid: A = (1/2) * (base1 + base2) * height. Step 3: Add the bases: 16 + 26 = 42. Step 4: Multiply by the height: 42 * 11 = 462. Step 5: Multiply by 1/2: 462 * 1/2 = 231. The area is 231 square centimeters.

2. A rectangular city park measures 120 meters by 80 meters. The city planners want to create a diagonal walking path that cuts across the park from one corner to the opposite corner, dividing the park into two triangular sections. They plan to plant flowers in one triangular section and leave the other as open lawn. What is the area of the section that will be planted with flowers? Answer: 4800 Solution: Find the area of the entire rectangular park. Area of rectangle = length × width = 120 m × 80 m = 9600 square meters Understand how the diagonal divides the rectangle.
   Full step-by-step solution

   Step 1: Find the area of the entire rectangular park. Area of rectangle = length × width = 120 m × 80 m = 9600 square meters Step 2: Understand how the diagonal divides the rectangle. A diagonal line from one corner of a rectangle to the opposite corner divides the rectangle into two congruent triangles of equal area. Step 3: Calculate the area of one triangular section. Since both triangles have equal area, each triangle's area is half of the rectangle's area. Area of one triangle = 9600 ÷ 2 = 4800 square meters Step 4: Identify which section is planted. The problem asks for the area of the section that will be planted with flowers, which is one of the two triangular sections. The area of the planted section is 4800 square meters.

3. A rectangular garden has a length of 12.5 m and a width of 8.4 m. A triangular flower bed inside it has a base of 5 m and a height of 3.2 m. What is the area of the garden not covered by the flower bed? Answer: 97 Solution: Find the area of the rectangular garden. Area = length × width Length = 12.5 m Width = 8.4 m Area of garden = 12.5 × 8.4 12.5 × 8 = 100 12.5 × 0.4 = 5 So 100 + 5 = 105 So, area of garden = 105 m² Find the area of the triangular flower bed.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the area of the rectangular garden.** The formula for the area of a rectangle is: Area = length × width Given: Length = 12.5 m Width = 8.4 m Area of garden = 12.5 × 8.4 First compute: 12.5 × 8 = 100 12.5 × 0.4 = 5 So 100 + 5 = 105 So, area of garden = 105 m² --- **Step 2: Find the area of the triangular flower bed.** The formula for the area of a triangle is: Area = (base × height) / 2 Given: Base = 5 m Height = 3.2 m Area of triangle = (5 × 3.2) / 2 First compute: 5 × 3.2 = 16 Then 16 / 2 = 8 So, area of flower bed = 8 m² --- **Step 3: Find the area of the garden not covered by the flower bed.** This is the garden area minus the flower bed area: Area not covered = 105 − 8 = 97 m² --- **Final Answer:** 97

4. Max is designing a parallelogram-shaped garden. The base of the garden is 8 meters and the height (the perpendicular distance between the bases) is 7 meters. How many square meters of grass seed will Max need to cover the entire garden? Answer: 56 Solution: Recall the formula for the area of a parallelogram: Area = base × height. Substitute the base = 8 meters and height = 7 meters: Area = 8 × 7. Multiply: 8 × 7 = 56.
   Full step-by-step solution

   Step 1: Recall the formula for the area of a parallelogram: Area = base × height. Step 2: Substitute the base = 8 meters and height = 7 meters: Area = 8 × 7. Step 3: Multiply: 8 × 7 = 56. Max will need 56 square meters of grass seed.

5. Olivia is designing a parallelogram-shaped garden. The base of the garden is 10 meters and the height (the perpendicular distance between the bases) is 20 meters. How many square meters of grass seed will Olivia need to cover the entire garden? Answer: 200 Solution: Recall the formula for the area of a parallelogram: Area = base × height. Substitute the base = 10 meters and height = 20 meters: Area = 10 × 20. Multiply: 10 × 20 = 200.
   Full step-by-step solution

   Step 1: Recall the formula for the area of a parallelogram: Area = base × height. Step 2: Substitute the base = 10 meters and height = 20 meters: Area = 10 × 20. Step 3: Multiply: 10 × 20 = 200. Olivia will need 200 square meters of grass seed.