Learn on PengienVision, Mathematics, Grade 6Chapter 7: Solve Area, Surface Area, and Volume Problems

Lesson 3: Find Areas of Trapezoids and Kites

In this Grade 6 enVision Mathematics lesson, students learn to find the areas of trapezoids and kites by decomposing them into familiar shapes such as rectangles and triangles, then adding or subtracting their areas. Students apply the formulas for triangle and rectangle area to calculate dimensions of real-world polygons, including irregular figures like building walls and kite-shaped windows. The lesson also introduces the strategy of composing two identical trapezoids into a parallelogram to derive the area of a single trapezoid.

Section 1

Area of a Trapezoid

Property

The area of a trapezoid with height hh and bases b1b_1 and b2b_2 is given by the formula:

A=12h(b1+b2)A = \frac{1}{2}h(b_1 + b_2)

Examples

  • A trapezoid with bases of length 66 and 1010 and a height of 44 has an area of:
A=12(4)(6+10)=12(4)(16)=32 square unitsA = \frac{1}{2}(4)(6 + 10) = \frac{1}{2}(4)(16) = 32 \text{ square units}
  • A trapezoid with bases of length 33 and 77 and a height of 55 has an area of:
A=12(5)(3+7)=12(5)(10)=25 square unitsA = \frac{1}{2}(5)(3 + 7) = \frac{1}{2}(5)(10) = 25 \text{ square units}

Explanation

A trapezoid is a quadrilateral with at least one pair of parallel sides, which are called the bases. The height of a trapezoid is the perpendicular distance between these two bases. To find the area, you add the lengths of the two bases, multiply by the height, and then divide by two. This is equivalent to finding the average of the bases and multiplying by the height.

Section 2

Area of a Kite

Property

The area of a kite is half the product of the lengths of its diagonals, d1d_1 and d2d_2.

A=12d1d2A = \frac{1}{2}d_1 d_2

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 7: Solve Area, Surface Area, and Volume Problems

  1. Lesson 1

    Lesson 1: Find Areas of Parallelograms and Rhombuses

    LearnPractice
  2. Lesson 2

    Lesson 2: Solve Triangle Area Problems

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Find Areas of Trapezoids and Kites

    LearnPractice
  4. Lesson 4

    Lesson 4: Find Areas of Polygons

    LearnPractice
  5. Lesson 5

    Lesson 5: Represent Solid Figures Using Nets

    LearnPractice
  6. Lesson 6

    Lesson 6: Find Surface Areas of Prisms

    LearnPractice
  7. Lesson 7

    Lesson 7: Find Surface Areas of Pyramids

    LearnPractice
  8. Lesson 8

    Lesson 8: Find Volume with Fractional Edge Lengths

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Area of a Trapezoid

Property

The area of a trapezoid with height hh and bases b1b_1 and b2b_2 is given by the formula:

A=12h(b1+b2)A = \frac{1}{2}h(b_1 + b_2)

Examples

  • A trapezoid with bases of length 66 and 1010 and a height of 44 has an area of:
A=12(4)(6+10)=12(4)(16)=32 square unitsA = \frac{1}{2}(4)(6 + 10) = \frac{1}{2}(4)(16) = 32 \text{ square units}
  • A trapezoid with bases of length 33 and 77 and a height of 55 has an area of:
A=12(5)(3+7)=12(5)(10)=25 square unitsA = \frac{1}{2}(5)(3 + 7) = \frac{1}{2}(5)(10) = 25 \text{ square units}

Explanation

A trapezoid is a quadrilateral with at least one pair of parallel sides, which are called the bases. The height of a trapezoid is the perpendicular distance between these two bases. To find the area, you add the lengths of the two bases, multiply by the height, and then divide by two. This is equivalent to finding the average of the bases and multiplying by the height.

Section 2

Area of a Kite

Property

The area of a kite is half the product of the lengths of its diagonals, d1d_1 and d2d_2.

A=12d1d2A = \frac{1}{2}d_1 d_2

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 7: Solve Area, Surface Area, and Volume Problems

  1. Lesson 1

    Lesson 1: Find Areas of Parallelograms and Rhombuses

    LearnPractice
  2. Lesson 2

    Lesson 2: Solve Triangle Area Problems

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Find Areas of Trapezoids and Kites

    LearnPractice
  4. Lesson 4

    Lesson 4: Find Areas of Polygons

    LearnPractice
  5. Lesson 5

    Lesson 5: Represent Solid Figures Using Nets

    LearnPractice
  6. Lesson 6

    Lesson 6: Find Surface Areas of Prisms

    LearnPractice
  7. Lesson 7

    Lesson 7: Find Surface Areas of Pyramids

    LearnPractice
  8. Lesson 8

    Lesson 8: Find Volume with Fractional Edge Lengths

    LearnPractice