Composite and Shaded Figures: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

Two rectangles have disjoint interiors and share part of an edge. Their dimensions are $8$ cm by $7$ cm and $3$ cm by $6$ cm. What is the area of their union?

Answer choices for question 1 A $38\text{ cm}^2$ B $74\text{ cm}^2$ C $92\text{ cm}^2$ D $143\text{ cm}^2$
2

A $16$ cm by $10$ cm rectangle has a $4$ cm by $3$ cm rectangular corner removed. What area remains?

Answer choices for question 2 A $172\text{ cm}^2$ B $12\text{ cm}^2$ C $84\text{ cm}^2$ D $148\text{ cm}^2$
3

A rectangle $11$ cm wide and $4$ cm high is joined to a triangle along the triangle's entire $11$ cm base. The triangle lies outside the rectangle and has perpendicular height $6$ cm. What is the combined area?

Answer choices for question 3 A $77\text{ cm}^2$ B $110\text{ cm}^2$ C $66\text{ cm}^2$ D $55\text{ cm}^2$
4

An L-shaped polygon has horizontal and vertical sides. Its full width is $22$ cm, and its upper horizontal side is $9$ cm. What is the horizontal width of the absent upper right corner?

Answer choices for question 4 A $31$ cm B $9$ cm C $13$ cm D $11$ cm
5

An L-shaped polygon has horizontal and vertical sides. Its full height is $15$ cm. The lower right vertical side is $6$ cm. What is the vertical depth of the absent upper right corner?

Answer choices for question 5 A $21$ cm B $6$ cm C $9$ cm D $2.5$ cm
6

Two polygons are joined along a segment, with disjoint interiors and no other contact. Which statement describes that segment in the union?

Answer choices for question 6 A It is internal and contributes no perimeter. B It contributes its length once to the perimeter. C It contributes twice its length to the perimeter. D It must be subtracted from the union area.
7

One centimeter equals $10$ millimeters. How many square millimeters make one square centimeter?

Answer choices for question 7 A $10$ B $20$ C $1000$ D $100$
8

Use $1$ m equal to $100$ cm. Express $6400$ square centimeters in square meters.

Answer choices for question 8 A $64\text{ m}^2$ B $0.64\text{ m}^2$ C $6.4\text{ m}^2$ D $640000\text{ m}^2$
9

A $13$ cm by $9$ cm rectangle contains a $5$ cm by $3$ cm rectangular hole strictly inside it. What is the retained area?

Answer choices for question 9 A $102\text{ cm}^2$ B $132\text{ cm}^2$ C $117\text{ cm}^2$ D $15\text{ cm}^2$
10

An $18$ cm by $14$ cm rectangular region contains a $6$ cm by $4$ cm rectangular hole strictly inside it. What is the total boundary length, including the hole?

Answer choices for question 10 A $64$ cm B $44$ cm C $84$ cm D $74$ cm
11

Two polygons with perimeters $28$ cm and $36$ cm have disjoint interiors and meet along exactly one $5$ cm segment. What is their union perimeter?

Answer choices for question 11 A $64$ cm B $54$ cm C $59$ cm D $74$ cm
12

When does subtracting the area of a removed polygon from the area of an outer polygon give the retained area?

Answer choices for question 12 A The two polygons have equal perimeters. B The removed polygon has more sides. C The two polygons are congruent, wherever they lie. D The removed polygon lies completely inside the outer polygon.