In quadrilateral ABCD shown in adjoining figure, AB || DC and AD I AB. Also, AB=8 m, DC = 5m. Find the area of the quadrilateral in two ways:(i) Taking ABCD as a trapezium.(ii) Taking quadrilateral ABCD as the sum ofrectangle AECD + triangle BEC.

In quadrilateral ABCD shown in adjoining figure, AB || DC and AD I AB.

1.	In quadrilateral ABCD shown in adjoining figure, AB \|\| DC and AD I AB. Also, AB=8 m, DC = 5m. Find the area of the quadrilateral in two ways:(i) Taking ABCD as a trapezium.(ii) Taking quadrilateral ABCD as the sum ofrectangle AECD + triangle BEC.
Answer» AB ║ CDAB ║ CDDA ⊥ABAB ║ CDDA ⊥ABAB = 8 mAB ║ CDDA ⊥ABAB = 8 mBC = 5 mAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ ABAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 MBE = AB - AE = 8 - 5 = 3 cmAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CEAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4AB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2AB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2= 26 m²AB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2= 26 m²Area of Quadrilateral ABCD = Area of RECTANGLE AECD + Area of Triangle BCEAB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2= 26 m²Area of Quadrilateral ABCD = Area of rectangle AECD + Area of Triangle BCEArea of rectangle AECD = AE * CE = 5 * 4 = 20 m²AB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2= 26 m²Area of Quadrilateral ABCD = Area of rectangle AECD + Area of Triangle BCEArea of rectangle AECD = AE * CE = 5 * 4 = 20 m²Area of Triangle BCE = (1/2)BE * CE = (1/2) * 3 * 4 = 6 m²AB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2= 26 m²Area of Quadrilateral ABCD = Area of rectangle AECD + Area of Triangle BCEArea of rectangle AECD = AE * CE = 5 * 4 = 20 m²Area of Triangle BCE = (1/2)BE * CE = (1/2) * 3 * 4 = 6 m²Area of Quadrilateral ABCD = 20 + 6 = 26 m²AB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2= 26 m²Area of Quadrilateral ABCD = Area of rectangle AECD + Area of Triangle BCEArea of rectangle AECD = AE * CE = 5 * 4 = 20 m²Area of Triangle BCE = (1/2)BE * CE = (1/2) * 3 * 4 = 6 m²Area of Quadrilateral ABCD = 20 + 6 = 26 m²Learn more:AB ║ CDDA ⊥ABAB = 8 mBC = 5 mCD = 5 mLet say CE ⊥ AB=> AE = CD = 5 mBE = AB - AE = 8 - 5 = 3 cmCE² = BC² - BE² = 5² - 3² = 25 - 9 = 16 = 4² => CE = 4 cmArea of Trapezium = (1/2)(AB + CD) * CE= (1/2)(8 + 5) * 4= 13 * 2= 26 m²Area of Quadrilateral ABCD = Area of rectangle AECD + Area of Triangle BCEArea of rectangle AECD = AE * CE = 5 * 4 = 20 m²Area of Triangle BCE = (1/2)BE * CE = (1/2) * 3 * 4 = 6 m²Area of Quadrilateral ABCD = 20 + 6 = 26 m²Learn more:There is a trapezium whose parallel sides are 10 cm and 22.3 CM ...If the area of a trapezium with parallel sides of length 30 cm and 23 ...In trapezium ABCD, AB \|\| CD and AC = BD.

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In quadrilateral ABCD shown in adjoining figure, AB || DC and AD I AB. Also, AB=8 m, DC = 5m. Find the area of the quadrilateral in two ways:(i) Taking ABCD as a trapezium.(ii) Taking quadrilateral ABCD as the sum ofrectangle AECD + triangle BEC.​

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In quadrilateral ABCD shown in adjoining figure, AB || DC and AD I AB. Also, AB=8 m, DC = 5m. Find the area of the quadrilateral in two ways:(i) Taking ABCD as a trapezium.(ii) Taking quadrilateral ABCD as the sum ofrectangle AECD + triangle BEC.