Grade 6 examples and questions on calculating areas of composite shapes and figures with detailed solutions and explanations are presented.
You first need to review the formulas to calculate areas for basic figures such as squares, rectangles, triangles, parallelograms and trapezoids.
Use the grid to determine the dimensions needed to and find the areas of the shapes shown below.
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The area A of the given shape is calculated using 3 steps:
1) calculate the area of the large rectangle ABWF :
A1 = Length × Width = 5 × 3 = 15 unit 2
2) Calculate the area of the small rectangle CWED :
A2 = CW × WE = 3 × 1 = 3 unit 2
3) Subtract the area of the small rectangle from that of the large rectangle:
A = A1 - A2 = 15 - 3 = 12 unit 2
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The area A of the given shape is calculated using 3 steps:
1) calculate the area of the large rectangle GHZL :
A1 = Length × Width = 5 × 3 = 15 unit 2
2) Calculate the area of the trapezoid JIZK :
A2 = (1/2) × ZK × (IZ + JK) = (1/2) × 1 ×(2 + 3)
= (1/2) × 1 × 5 = (1/2) 5 = 5 / 2 = 2.5 unit 2
3) Subtract the area of the trapezoid from that of the large rectangle:
A = A1 - A2 = 15 - 2.5 = 12.5 unit 2
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The area A of the given shape is calculated using 3 steps:
1) calculate the area of the large rectangle QMNP :
A1 = Length × Width = 5 × 3 = 15 unit 2
2) Calculate the area of the triangle NOP :
A2 = (1/2) × H × NP = (1/2) × 2 ×3
= (1/2) × 6 = 3 unit 2
3) Subtract the area of the triangle from that of the large rectangle:
A = A1 - A2 = 15 - 3 = 12 unit 2
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The area A of the given shape is calculated using 4 steps:
1) calculate the area of the large rectangle RA1BS :
A1 = Length × Width = 6 × 3 = 18 unit 2
2) Calculate the area of the triangle RA1V :
A2 = (1/2) × RA1 × A1V = (1/2) × 3 ×2 = (1/2) × 6 = 3 unit 2
3) Calculate the area of the triangle UBT :
A3 = (1/2) × UB× BT = (1/2) × 1 ×1 = (1/2) = 0.5 unit 2
3) Subtract the areas of the two triangles from that of the large rectangle:
A = A1 - A2 - A3 = 18 - 3 - 0.5 = 14,5 unit 2