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Composite and Shaded Figures: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

An orthogonal polygon is formed by removing an upper right rectangular corner $12$ cm wide and $9$ cm deep from a $27$ cm by $16$ cm rectangle. Find its area and perimeter.

Answer choices for question 1 A
$324\text{ cm}^2$

$128$ cm
B
$540\text{ cm}^2$

$86$ cm
C
$324\text{ cm}^2$

$86$ cm
D
$324\text{ cm}^2$

$44$ cm
2

A $20$ cm by $15$ cm rectangle contains a triangular hole strictly inside it. The hole has sides $10$ cm, $10$ cm, and $12$ cm. What is the total boundary length, including the hole?

Answer choices for question 2 A $102$ cm B $70$ cm C $38$ cm D $92$ cm
3

Two polygonal regions have areas $96$ and $77$ square centimeters. Their common part has area $22$ square centimeters. What is the area of their union?

Answer choices for question 3 A $173\text{ cm}^2$ B $195\text{ cm}^2$ C $129\text{ cm}^2$ D $151\text{ cm}^2$
4

A $25$ cm by $17$ cm rectangle loses a $10$ cm by $7$ cm rectangular corner. All remaining sides are horizontal or vertical. What is the perimeter of the remaining region?

Answer choices for question 4 A $50$ cm B $84$ cm C $118$ cm D $67$ cm
5

A $12$ cm by $7$ cm rectangle and a right triangle with legs $12$ cm and $5$ cm are joined along their full $12$ cm sides. Their interiors are disjoint. Find the union area and perimeter.

Answer choices for question 5 A
$114\text{ cm}^2$

$44$ cm
B
$144\text{ cm}^2$

$44$ cm
C
$114\text{ cm}^2$

$56$ cm
D
$114\text{ cm}^2$

$68$ cm
6

A $29$ cm by $12$ cm rectangle has an upper right rectangular notch $6$ cm wide and $x$ cm deep. The retained area is $282$ square centimeters. What is $x$ ?

Answer choices for question 6 A $47$ cm B $6$ cm C $9$ cm D $11$ cm
7

Use $1$ foot equal to $12$ inches. How many square inches is $2.25$ square feet?

Answer choices for question 7 A $27\text{ in}^2$ B $324\text{ in}^2$ C $54\text{ in}^2$ D $0.015625\text{ in}^2$
8

A rectangle measures $1.3$ m by $75$ cm. A $20$ cm by $30$ cm rectangular hole lies strictly inside it. Use $1$ m equal to $100$ cm. What area remains in square centimeters?

Answer choices for question 8 A $-502.5\text{ cm}^2$ B $10350\text{ cm}^2$ C $9150\text{ cm}^2$ D $9750\text{ cm}^2$
9

A room has the outline of a $6.2$ m by $4.7$ m rectangle with a $2.4$ m by $1.5$ m corner removed. All edges meet at right angles. Baseboard covers the entire room boundary except a $0.9$ m doorway on one edge. What length is needed?

Answer choices for question 9 A $21.8$ m B $13.1$ m C $28.7$ m D $20.9$ m
10

A $17$ cm by $12$ cm rectangle surrounds a rectangular hole. A border $2$ cm wide separates the hole from each of the four outer sides. What is the border area?

Answer choices for question 10 A $54\text{ cm}^2$ B $100\text{ cm}^2$ C $104\text{ cm}^2$ D $204\text{ cm}^2$
11

A trapezoid has parallel bases $15$ cm and $9$ cm and perpendicular height $8$ cm. A triangular hole of base $6$ cm and perpendicular height $5$ cm lies strictly inside. What is the retained area?

Answer choices for question 11 A $111\text{ cm}^2$ B $66\text{ cm}^2$ C $81\text{ cm}^2$ D $177\text{ cm}^2$
12

One yard equals $3$ feet. Which conversion and reason are correct?

Answer choices for question 12 A $7\text{ yd}^2=63\text{ ft}^2$ , because each square yard contains $3$ rows of $3$ square feet. B $7\text{ yd}^2=21\text{ ft}^2$ , because each yard contains $3$ feet. C $7\text{ yd}^2=42\text{ ft}^2$ , because a square has two directions. D $7\text{ yd}^2=189\text{ ft}^2$ , because three feet requires three factors.

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