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Triangle/Quad Area

Grade 6 · Geometry · Worksheet 2

  1. A rectangular garden measures 15 meters by 12 meters. A triangular pond is built in one corner of the garden, with its right angle at the corner. The two sides forming the right angle extend 4 meters along the length and 3 meters along the width. What is the area of the garden that remains for planting?
    Answer: ______________
  2. Aroha is designing a kite. One part is a triangle with a base of 13 cm and a height of 9 cm. Another part is a parallelogram with a base of 15 cm and a height of 7 cm. What is the total area of both shapes in square centimeters? Answer: ______________
  3. Liam is designing a triangular garden with a base of 12 meters and a height of 8 meters. He also wants to create a rectangular flower bed that is 5 meters long and 3 meters wide. What is the total area, in square meters, that Liam will need for his garden and flower bed combined? Answer: ______________
  4. Liam is designing a banner for the school fair that consists of a large rectangle with a triangular pennant attached to its top. The rectangular part measures 2.4 meters long and 1.2 meters wide. The triangular pennant has a base equal to the rectangle's length and a height of 0.8 meters. What is the total area of Liam's banner design in square meters?
    Answer: ______________
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Answer Key & Explanations

Triangle/Quad Area · Grade 6 · Worksheet 2

  1. A rectangular garden measures 15 meters by 12 meters. A triangular pond is built in one corner of the garden, with its right angle at the corner. The two sides forming the right angle extend 4 meters along the length and 3 meters along the width. What is the area of the garden that remains for planting? Answer: 174 Solution: Calculate the area of the rectangular garden. Area of rectangle = length × width = 15 m × 12 m = 180 square meters Calculate the area of the triangular pond.
    Full step-by-step solution

    Step 1: Calculate the area of the rectangular garden. Area of rectangle = length × width = 15 m × 12 m = 180 square meters Step 2: Calculate the area of the triangular pond. The triangle has legs of 4 m and 3 m (the sides forming the right angle). Area of triangle = (1/2) × base × height = (1/2) × 4 m × 3 m = (1/2) × 12 = 6 square meters Step 3: Subtract the pond area from the total garden area. Remaining area = 180 square meters - 6 square meters = 174 square meters The answer is 174 square meters.

  2. Aroha is designing a kite. One part is a triangle with a base of 13 cm and a height of 9 cm. Another part is a parallelogram with a base of 15 cm and a height of 7 cm. What is the total area of both shapes in square centimeters? Answer: 163.5 Solution: Calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 13 × 9 = 1/2 × 117 = 58.5 square cm. Calculate the area of the parallelogram.
    Full step-by-step solution

    Step 1: Calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 13 × 9 = 1/2 × 117 = 58.5 square cm. Step 2: Calculate the area of the parallelogram. Area = base × height = 15 × 7 = 105 square cm. Step 3: Add the two areas together. Total area = 58.5 + 105 = 163.5 square cm. The answer is 163.5.

  3. Liam is designing a triangular garden with a base of 12 meters and a height of 8 meters. He also wants to create a rectangular flower bed that is 5 meters long and 3 meters wide. What is the total area, in square meters, that Liam will need for his garden and flower bed combined? Answer: 63 Solution: Area = (base × height) / 2 Given: base = 12 m, height = 8 m Area_triangle = (12 × 8) / 2 Area_triangle = 96 / 2 Area_triangle = 48 square meters Area = length × width Given: length = 5 m, width = 3 m Area_rectangle = 5 × 3 Area_rectangle = 15 square meters Total area = Area_triangle +…
    Full step-by-step solution

    Let's solve this step by step. --- **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_triangle = (12 × 8) / 2 Area_triangle = 96 / 2 Area_triangle = 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_rectangle = 5 × 3 Area_rectangle = 15 square meters --- **Step 3: Find the total area** Total area = Area_triangle + Area_rectangle Total area = 48 + 15 Total area = 63 square meters --- **Final Answer:** 63

  4. Liam is designing a banner for the school fair that consists of a large rectangle with a triangular pennant attached to its top. The rectangular part measures 2.4 meters long and 1.2 meters wide. The triangular pennant has a base equal to the rectangle's length and a height of 0.8 meters. What is the total area of Liam's banner design in square meters? Answer: 3.84 Solution: Calculate the area of the rectangular part. Area of rectangle = length × width = 2.4 m × 1.2 m = 2.88 square meters Calculate the area of the triangular pennant.
    Full step-by-step solution

    Step 1: Calculate the area of the rectangular part. Area of rectangle = length × width = 2.4 m × 1.2 m = 2.88 square meters Step 2: Calculate the area of the triangular pennant. Area of triangle = (1/2) × base × height = (1/2) × 2.4 m × 0.8 m = (1/2) × 1.92 = 0.96 square meters Step 3: Add the areas together to find the total area. Total area = area of rectangle + area of triangle = 2.88 + 0.96 = 3.84 square meters The answer is 3.84.