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Questions and Answers
What is the calculated area of square [ABCD] using the formula $\text{Area}[ABCD] = (AB + DC) / 2 * BC$?
What is the calculated area of square [ABCD] using the formula $\text{Area}[ABCD] = (AB + DC) / 2 * BC$?
- 24 cm² (correct)
- 36 cm²
- 40 cm²
- 30 cm²
What is the area of quadrilateral [AFCD]?
What is the area of quadrilateral [AFCD]?
- 13.5 cm² (correct)
- 22.5 cm²
- 24.5 cm²
- 27 cm²
How is the area of [ABEF] first calculated?
How is the area of [ABEF] first calculated?
- By adding the areas of [AFD] and [FCE] to that of [ABCD]
- By subtracting areas of [AFD] and [FCE] from that of [ABCD] (correct)
- By using the formula of a triangle
- By multiplying the lengths of AB and BE
Which dimensions are used in the calculation of area [ABCD] when using $AB * BE$?
Which dimensions are used in the calculation of area [ABCD] when using $AB * BE$?
What is the final area of [ABEF] as calculated?
What is the final area of [ABEF] as calculated?
Flashcards
Area of a Square
Area of a Square
The area of square ABCD calculated as side length squared.
Area Calculation Method
Area Calculation Method
Utilizing different dimensions to find area through various formulas.
Area [ABEF]
Area [ABEF]
The final area calculated is 22.5 cm² for figure ABEF.
Error Identification
Error Identification
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Quadrilateral Area
Quadrilateral Area
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Study Notes
Area of a Square and Rectangle
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ABCD is a square with sides AB = BC = CD = DA = 8 cm
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The side lengths are also AB = CD = 6 cm, AD = BC = 6 cm
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The area of a square is found by multiplying the side length by itself (AB X BC)
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The area of a square ABCD with sides of 8cm each is: (8cm + 8cm)/2 = 8 cm x 4 cm = 32 cm2
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The area of a rectangle is found by multiplying the length by the width
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The Area of the square [ABCD] = (AB + DC) / 2 x BC = (8 + 4)/2 x 4 = 24 cm2
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Another way to calculate the area of the square ABCD is: AB x BC = 8cm x 4cm = 24cm2
Area of a Triangle
- The area of a triangle is calculated by multiplying the base by half the height (base x height / 2 )
- The area of a triangle [ABE] is AB X BE = 7cm x 3.5 cm = 24.5 cm2
- Area (AFCD) = Area of square [ABCD] - Area[ABCF]
Area of a Trapezoid and Combined Shapes
- Area(AFCD) = Area(ABCD)/2 - Area(ABCF)
- (DB X AC / 2)-(FB X AC / 2)=9 x 9/2 - 6 x 9/2 = 81/2 - 54/2 = 40.5 - 27 = 13.5 cm2
- Area [ABEF] = Area(ABCD) - (Area AFD + Area FCE) = 6 x 6 - ((6 x 3)/2 + (3 x 3)/2) = 36 - (18/2 + 9/2) = 36 - (9 + 4.5) = 36 - 13.5 = 22.5 cm2
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