Geometry Practice Test: Area and Perimeter of Plane Figures
- Area and Perimeter
- 10 questions
- 14 minutes
Questions mix formulas with composite figures and scale changes. Tip: in composite shapes, check which edges are really on the outside before adding a perimeter.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A parallelogram has a base of 12 cm, a slanted side of 8 cm and a height of 6 cm.
What is its area?
Correct answer: D
Area of a parallelogram is base × height: 12 · 6 = 72 cm². Multiplying by the slanted side, 12 · 8 = 96, uses a length that is not perpendicular to the base.
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Question 2
A circle has a circumference of 18π inches.
What is its area?
Correct answer: B
From 2πr = 18π, r = 9, so the area is π · 9² = 81π in². Using 18 as the radius gives 324π.
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Question 3
The diagonals of a rhombus are 14 m and 9 m long.
What is the area of the rhombus?
Correct answer: A
The area of a rhombus is half the product of its diagonals: (14 · 9)/2 = 63 m². The value 126 m² forgets to halve.
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Question 4
A rectangle has a perimeter of 46 ft and a length of 15 ft.
What is its area?
Correct answer: C
Two widths are 46 − 2 · 15 = 16 ft, so the width is 8 ft and the area is 15 · 8 = 120 ft². Using 31 as the width (46 − 15) gives 465 ft².
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Question 5
What is the area of an equilateral triangle with sides of 8 cm?
Correct answer: B
The height is 43 cm (a 30-60-90 triangle), so the area is ½ · 8 · 43 = 163 cm². The formula (3/4)s² gives the same result.
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Question 6
Each side of a square is tripled. By what factor is the area multiplied?
Correct answer: D
Area scales by the square of the scale factor: 3² = 9. The factor 27 is the change for volume, not area.
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Question 7
A 4 m by 4 m square is cut out of one corner of a 20 m by 12 m rectangle.
What is the perimeter of the remaining shape?
Correct answer: B
Cutting a corner removes 4 m from two sides but adds two new inside edges of 4 m each, so the perimeter stays 2(20 + 12) = 64 m. Subtracting 8 m gives 56 m, which forgets the new edges.
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Question 8
A running field is a 100 m by 60 m rectangle with a semicircle attached to each 60 m end.
To the nearest tenth of a meter, what is the distance once around the outside of the field?
Correct answer: C
The outside is two 100 m straight sides plus two semicircles of diameter 60 m, which together make one full circle: 200 + 60π ≈ 388.5 m. The value 294.2 m uses only one semicircle.
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Question 9
A square is inscribed in a circle with radius 5 cm, so its corners lie on the circle.
To the nearest tenth, what is the area of the region inside the circle but outside the square?
Correct answer: A
The square's diagonal is the diameter, 10 cm, so its area is 10²/2 = 50 cm². The circle's area is 25π ≈ 78.5 cm², and 78.5 − 50 ≈ 28.5 cm².
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Question 10
A triangle has sides of 13, 14 and 15 units. The altitude to the side of length 14 is 12 units long.
What is the area of the triangle?
Correct answer: D
Area = ½ · base · height = ½ · 14 · 12 = 84 square units. Forgetting the ½ gives 168; the side 13 or 15 is not the height for base 14.
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