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Triangle/Quad Area

Grade 6 · Geometry · Worksheet 2

  1. Mia is building a kite in the shape of a parallelogram. The base of the kite measures 36 inches and the vertical height (the perpendicular distance between the top and bottom edges) measures 14 inches. How much fabric, in square inches, does Mia need to cover the kite? Answer: ______________
  2. A rectangular garden has a length of 15.2 m and a width of 10.5 m. A triangular flower bed with a base of 6.4 m and a height of 4.8 m is removed from it. What is the remaining area in m²?
    Answer: ______________
  3. 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 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: ______________
  4. A triangle has a base of 23 cm and a height of 15 cm. A parallelogram shares the same base and has a height of 11 cm. Find the total area of both shapes in square centimeters. Answer: ______________
  5. Matiu draws a triangle with a base of 24 cm and a height of 18 cm. What is its area in square centimeters? Answer: ______________
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Answer Key & Explanations

Triangle/Quad Area · Grade 6 · Worksheet 2

  1. Mia is building a kite in the shape of a parallelogram. The base of the kite measures 36 inches and the vertical height (the perpendicular distance between the top and bottom edges) measures 14 inches. How much fabric, in square inches, does Mia need to cover the kite? Answer: 504 Solution: The formula for the area of a parallelogram is A = base × height. Substitute the values: A = 36 × 14 Multiply: 36 × 14 = 504 The answer is 504 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 = 36 × 14 Step 3: Multiply: 36 × 14 = 504 The answer is 504 square inches.

  2. A rectangular garden has a length of 15.2 m and a width of 10.5 m. A triangular flower bed with a base of 6.4 m and a height of 4.8 m is removed from it. What is the remaining area in m²? Answer: 144.24 Solution: Calculate the area of the rectangular garden. Area of rectangle = length × width = 15.2 m × 10.5 m 15.2 × 10.5 = 159.6 So the rectangular garden area is 159.6 m². Calculate the area of the triangular flower bed.
    Full step-by-step solution

    Step 1: Calculate the area of the rectangular garden. Area of rectangle = length × width = 15.2 m × 10.5 m 15.2 × 10.5 = 159.6 So the rectangular garden area is 159.6 m². Step 2: Calculate the area of the triangular flower bed. Area of triangle = (base × height) ÷ 2 = (6.4 m × 4.8 m) ÷ 2 6.4 × 4.8 = 30.72 30.72 ÷ 2 = 15.36 So the triangular flower bed area is 15.36 m². Step 3: Calculate the remaining area by subtracting the triangle's area from the rectangle's area. Remaining area = 159.6 m² - 15.36 m² = 144.24 m² The answer is 144.24 m².

  3. 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 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: Find the area of the triangular garden. Area = (base × height) / 2 Here, base = 12 m, height = 8 m. So, Area of triangle = (12 × 8) / 2 = 96 / 2 = 48 square meters.
    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 Here, base = 12 m, height = 8 m. So, Area of triangle = (12 × 8) / 2 = 96 / 2 = 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. So, Area of rectangle = 10 × 7 = 70 square meters. Step 3: Add the two areas to get the total area. Total area = Area of triangle + Area of rectangle = 48 + 70 = 118 square meters. Final answer: 118

  4. A triangle has a base of 23 cm and a height of 15 cm. A parallelogram shares the same base and has a height of 11 cm. Find the total area of both shapes in square centimeters. Answer: 425.5 Solution: Find the area of the triangle. Area of triangle = 1/2 × base × height = 1/2 × 23 × 15 = 1/2 × 345 = 172.5 square cm. Find the area of the parallelogram.
    Full step-by-step solution

    Step 1: Find the area of the triangle. Area of triangle = 1/2 × base × height = 1/2 × 23 × 15 = 1/2 × 345 = 172.5 square cm. Step 2: Find the area of the parallelogram. Area of parallelogram = base × height = 23 × 11 = 253 square cm. Step 3: Add the areas together. Total area = 172.5 + 253 = 425.5 square cm. The answer is 425.5.

  5. Matiu draws a triangle with a base of 24 cm and a height of 18 cm. What is its area in square centimeters? Answer: 216 Solution: Recall the formula for the area of a triangle: A = 1/2 × base × height. Substitute the given values: base = 24 cm, height = 18 cm. Multiply the base and height: 24 × 18 = 432.
    Full step-by-step solution

    Step 1: Recall the formula for the area of a triangle: A = 1/2 × base × height. Step 2: Substitute the given values: base = 24 cm, height = 18 cm. Step 3: Multiply the base and height: 24 × 18 = 432. Step 4: Take half of that product: 432 ÷ 2 = 216. Step 5: The area is 216 square centimeters. The answer is 216.