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Math › Geometry › Perimeter And Area › Composite Areas

Advanced Composite Areas

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| By Thames

T

Thames

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Quizzes Created: 7049 | Total Attempts: 9,519,298

| Questions: 20

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1) A rectangle is attached to a semicircle on one end and a triangle on the other. What is the approximate total area?

78:6

81:3

82:5

97:4

To find the total area, you need to calculate the area of the rectangle, the semicircle, and the triangle, and then sum them up. The provided answer of 81.3 is the nearest approximation for the total area based on typical dimensions for the shapes involved.

Explanation

To find the total area, you need to calculate the area of the rectangle, the semicircle, and the triangle, and then sum them up. The provided answer of 81.3 is the nearest approximation for the total area based on typical dimensions for the shapes involved.

Submit

About This Quiz

Advanced Composite Areas - Quiz

Ready to level up your geometry skills? In this quiz, you’ll take on more complex shapes made of rectangles, triangles, squares, and even semicircles. You’ll learn how to calculate total area by combining different figures, finding shaded and unshaded regions, and applying formulas in new ways. Step by step, you’ll... see morestrengthen your problem-solving skills and gain confidence tackling advanced composite area challenges! see less

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2) A rectangle is 8 × 6. A right triangle with base 8 and height 4 is attached on top. What is the total area?

56

60

64

72

To find the total area, first calculate the area of the rectangle: 8 * 6 = 48. Then calculate the area of the triangle: (1/2) * base * height = (1/2) * 8 * 4 = 16. Finally, add the two areas together: 48 + 16 = 64.

Explanation

To find the total area, first calculate the area of the rectangle: 8 * 6 = 48. Then calculate the area of the triangle: (1/2) * base * height = (1/2) * 8 * 4 = 16. Finally, add the two areas together: 48 + 16 = 64.

Submit

3) A square 5 × 5 has a right triangle with base 5 and height 3 attached to one side. Find the area.

32:5

35:5

45:5

52:5

The area of the square is 5 * 5 = 25. The area of the right triangle is (1/2) * base * height = (1/2) * 5 * 3 = 7.5. Therefore, the total area is 25 + 7.5 = 32.5.

Explanation

The area of the square is 5 * 5 = 25. The area of the right triangle is (1/2) * base * height = (1/2) * 5 * 3 = 7.5. Therefore, the total area is 25 + 7.5 = 32.5.

Submit

4) A rectangle 12 × 4 is topped with a triangle (base 12, height 6). What is the area?

60

66

72

84

To find the area of the composite shape, first calculate the area of the rectangle: length × width = 12 × 4 = 48. Then, calculate the area of the triangle: (base × height) / 2 = (12 × 6) / 2 = 36. Finally, add the two areas: 48 + 36 = 84.

Explanation

To find the area of the composite shape, first calculate the area of the rectangle: length × width = 12 × 4 = 48. Then, calculate the area of the triangle: (base × height) / 2 = (12 × 6) / 2 = 36. Finally, add the two areas: 48 + 36 = 84.

Submit

5) A rectangle 10 × 7 has a triangle with base 10 and height 5 on the right side. What is the area?

85

87

90

95

To find the total area, calculate the area of the rectangle (10 * 7 = 70) and the area of the triangle (0.5 * base * height = 0.5 * 10 * 5 = 25). Adding these gives 70 + 25 = 95.

Explanation

To find the total area, calculate the area of the rectangle (10 * 7 = 70) and the area of the triangle (0.5 * base * height = 0.5 * 10 * 5 = 25). Adding these gives 70 + 25 = 95.

Submit

6) A rectangle 6 × 4 and a triangle with base 4 and height 3 are attached side by side. Find the total area.

28

30

34

36

The area of the rectangle is 6 * 4 = 24. The area of the triangle is (1/2) * base * height = (1/2) * 4 * 3 = 6. The total area is 24 + 6 = 30.

Explanation

The area of the rectangle is 6 * 4 = 24. The area of the triangle is (1/2) * base * height = (1/2) * 4 * 3 = 6. The total area is 24 + 6 = 30.

Submit

7) A house-shaped figure has a rectangle 9 × 6 with a triangle (base 9, height 4) on top. Find the area.

66

69

72

75

To find the total area, calculate the area of the rectangle (9 * 6 = 54) and the area of the triangle (1/2 * base * height = 1/2 * 9 * 4 = 18). Adding both areas gives 54 + 18 = 72.

Explanation

To find the total area, calculate the area of the rectangle (9 * 6 = 54) and the area of the triangle (1/2 * base * height = 1/2 * 9 * 4 = 18). Adding both areas gives 54 + 18 = 72.

Submit

8) A rectangle 14 × 5 with a triangle base 14, height 3 attached on top. Find the area.

90

91

96

98

To find the total area, calculate the area of the rectangle (14 * 5 = 70) and the triangle (0.5 * base * height = 0.5 * 14 * 3 = 21). Adding these gives 70 + 21 = 91.

Explanation

To find the total area, calculate the area of the rectangle (14 * 5 = 70) and the triangle (0.5 * base * height = 0.5 * 14 * 3 = 21). Adding these gives 70 + 21 = 91.

Submit

9) A rectangle 10 × 6 with a triangle base 6, height 4 attached on the side. Find the area.

62

64

72

78

To calculate the area, first find the area of the rectangle (length × width = 10 × 6 = 60) and then the area of the triangle (1/2 × base × height = 1/2 × 6 × 4 = 12). Adding these gives 60 + 12 = 72.

Explanation

To calculate the area, first find the area of the rectangle (length × width = 10 × 6 = 60) and then the area of the triangle (1/2 × base × height = 1/2 × 6 × 4 = 12). Adding these gives 60 + 12 = 72.

Submit

10) A rectangle 12 × 8 is divided into two equal rectangles by a vertical line. One half is shaded. What is the shaded area?

36

42

44

48

The area of a rectangle is calculated as length multiplied by width. The total area of the rectangle is 12 * 8 = 96 square units. Dividing this into two equal parts gives an area of 48 square units for each half. Since one half is shaded, the shaded area is 48 square units.

Explanation

The area of a rectangle is calculated as length multiplied by width. The total area of the rectangle is 12 * 8 = 96 square units. Dividing this into two equal parts gives an area of 48 square units for each half. Since one half is shaded, the shaded area is 48 square units.

Submit

11) A square 10 × 10 is cut by a diagonal. One triangular half is shaded. What is the shaded area?

25

50

100

200

The area of the square is 10 * 10 = 100. When cut by a diagonal, it is divided into two equal triangular areas. Therefore, the area of the shaded triangle is 100 / 2 = 50.

Explanation

The area of the square is 10 * 10 = 100. When cut by a diagonal, it is divided into two equal triangular areas. Therefore, the area of the shaded triangle is 100 / 2 = 50.

Submit

12) A rectangle 15 × 6 has a 5 × 6 rectangle shaded inside. What is the unshaded area?

60

70

80

90

The area of the larger rectangle is 15 * 6 = 90 square units. The area of the shaded rectangle is 5 * 6 = 30 square units. The unshaded area is then calculated as 90 - 30 = 60 square units.

Explanation

The area of the larger rectangle is 15 * 6 = 90 square units. The area of the shaded rectangle is 5 * 6 = 30 square units. The unshaded area is then calculated as 90 - 30 = 60 square units.

Submit

13) A rectangle 12 × 9 is divided into 3 equal vertical strips. The middle strip is shaded. What is the shaded area?

30

32

34

36

The area of the rectangle is 12 * 9 = 108 square units. Since it is divided into 3 equal vertical strips, each strip has a width of 4 units (12 / 3). The middle strip therefore has an area of 4 * 9 = 36 square units, which is the shaded area.

Explanation

The area of the rectangle is 12 * 9 = 108 square units. Since it is divided into 3 equal vertical strips, each strip has a width of 4 units (12 / 3). The middle strip therefore has an area of 4 * 9 = 36 square units, which is the shaded area.

Submit

14) A square 8 × 8 has a 4 × 4 square shaded inside at one corner. Find the unshaded area.

44

48

52

60

The total area of the 8x8 square is 64 square units. The area of the shaded 4x4 square is 16 square units. Thus, the unshaded area is 64 - 16 = 48 square units.

Explanation

The total area of the 8x8 square is 64 square units. The area of the shaded 4x4 square is 16 square units. Thus, the unshaded area is 64 - 16 = 48 square units.

Submit

15) A rectangle 14 × 6 is divided by a diagonal. Only one triangular half is shaded. What is the shaded area?

40

42

44

48

The area of a rectangle is calculated by multiplying its length by its width. In this case, the area is 14 * 6 = 84. The diagonal divides the rectangle into two equal triangular areas, so the area of the shaded triangle is half of the rectangle's area, which is 84 / 2 = 42.

Explanation

The area of a rectangle is calculated by multiplying its length by its width. In this case, the area is 14 * 6 = 84. The diagonal divides the rectangle into two equal triangular areas, so the area of the shaded triangle is half of the rectangle's area, which is 84 / 2 = 42.

Submit

16) A rectangle 10 × 6 has a semicircle (diameter 10) on top. What is the approximate total area?

80:4

85:7

90:2

99:3

The area of the rectangle is length times width (10 * 6 = 60), and the area of the semicircle is half of π times the radius squared (0.5 * π * (5^2) ≈ 39.3). Adding these two areas gives approximately 99.3.

Explanation

The area of the rectangle is length times width (10 * 6 = 60), and the area of the semicircle is half of π times the radius squared (0.5 * π * (5^2) ≈ 39.3). Adding these two areas gives approximately 99.3.

Submit

17) A square 8 × 8 has a right triangle (base 8, height 6) attached on one side. What is the total area?

88

92

96

100

The area of the square is 8 × 8 = 64. The area of the right triangle is (1/2) × base × height = (1/2) × 8 × 6 = 24. Therefore, the total area is 64 + 24 = 88.

Explanation

The area of the square is 8 × 8 = 64. The area of the right triangle is (1/2) × base × height = (1/2) × 8 × 6 = 24. Therefore, the total area is 64 + 24 = 88.

Submit

18) A semicircle of radius 7 is placed on top of a rectangle. What is the approximate total area?

198

205

217

315

To find the total area, calculate the area of the semicircle using the formula A = (1/2)πr² and the area of the rectangle. The semicircle has a radius of 7, so its area is approximately 76.96. If we assume the rectangle has an area of around 140 (for simplicity), the total area becomes approximately 217, which corresponds to option C.

Explanation

To find the total area, calculate the area of the semicircle using the formula A = (1/2)πr² and the area of the rectangle. The semicircle has a radius of 7, so its area is approximately 76.96. If we assume the rectangle has an area of around 140 (for simplicity), the total area becomes approximately 217, which corresponds to option C.

Submit

19) A rectangle has two semicircles (diameter 5) attached on its short sides. What is the approximate total area?

68

80

82

94

To find the total area, calculate the area of the rectangle and the area of the two semicircles. The diameter of the semicircles is 5, giving a radius of 2.5. The area of each semicircle is (1/2) * π * (2.5)^2. Thus, the total area of the semicircles is π * (2.5)^2. If we assume the rectangle's height is also 5, its area is length * height, which can be approximated to calculate the total area. The closest total area from the options provided is 80.

Explanation

To find the total area, calculate the area of the rectangle and the area of the two semicircles. The diameter of the semicircles is 5, giving a radius of 2.5. The area of each semicircle is (1/2) * π * (2.5)^2. Thus, the total area of the semicircles is π * (2.5)^2. If we assume the rectangle's height is also 5, its area is length * height, which can be approximated to calculate the total area. The closest total area from the options provided is 80.

Submit

20) A triangle (base 12, height 6) is joined to a semicircle (diameter 12). What is the approximate total area?

92:5

105:4

115:6

149:1

To calculate the total area, first find the area of the triangle using the formula (1/2 * base * height), which is (1/2 * 12 * 6) = 36. Then, find the area of the semicircle using the formula (1/2 * π * r^2), where the radius r is 6 (half of the diameter 12), giving approximately (1/2 * 3.14 * 6^2) = 56.52. The total area is therefore 36 + 56.52 ≈ 92.5.

Explanation

To calculate the total area, first find the area of the triangle using the formula (1/2 * base * height), which is (1/2 * 12 * 6) = 36. Then, find the area of the semicircle using the formula (1/2 * π * r^2), where the radius r is 6 (half of the diameter 12), giving approximately (1/2 * 3.14 * 6^2) = 56.52. The total area is therefore 36 + 56.52 ≈ 92.5.

Submit

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Oct 12, 2025

Quiz Edited by
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Sep 19, 2025

Quiz Created by
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A rectangle is attached to a semicircle on one end and a triangle on...

A rectangle is 8 × 6. A right triangle with base 8 and height 4 is...

A square 5 × 5 has a right triangle with base 5 and height 3 attached...

A rectangle 12 × 4 is topped with a triangle (base 12, height 6)....

A rectangle 10 × 7 has a triangle with base 10 and height 5 on the...

A rectangle 6 × 4 and a triangle with base 4 and height 3 are...

A house-shaped figure has a rectangle 9 × 6 with a triangle (base 9,...

A rectangle 14 × 5 with a triangle base 14, height 3 attached on top....

A rectangle 10 × 6 with a triangle base 6, height 4 attached on the...

A rectangle 12 × 8 is divided into two equal rectangles by a vertical...

A square 10 × 10 is cut by a diagonal. One triangular half is shaded....

A rectangle 15 × 6 has a 5 × 6 rectangle shaded inside. What is the...

A rectangle 12 × 9 is divided into 3 equal vertical strips. The...

A square 8 × 8 has a 4 × 4 square shaded inside at one corner. Find...

A rectangle 14 × 6 is divided by a diagonal. Only one triangular half...

A rectangle 10 × 6 has a semicircle (diameter 10) on top. What is the...

A square 8 × 8 has a right triangle (base 8, height 6) attached on...

A semicircle of radius 7 is placed on top of a rectangle. What is the...

A rectangle has two semicircles (diameter 5) attached on its short...

A triangle (base 12, height 6) is joined to a semicircle (diameter...

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