Geo (9): Quadrilaterals
120
From The College Panda ACT Math: Advanced Guide and Workbook (p. 127)¹: A rectangle with a length of 6 centimeters has the same area as a square with side length 18 centimeters. What is the perimeter, in centimeters of the rectangle?
125
From The College Panda ACT Math: Advanced Guide and Workbook (p. 127)¹: In the figure below, all the adjacent line segments intersect in right angles, and all segments have the same length. If the perimeter of the figure is 60 units long, what is the area, in square units, of the entire figure?
22
From The College Panda ACT Math: Advanced Guide and Workbook (p. 127)¹: The perimeter of a rectangle is 94 inches. The length of the rectangle is 3 inches shorter than the width. What is the length of the rectangle, in inches?
51
From The College Panda ACT Math: Advanced Guide and Workbook (p. 127)¹: Trapezoid ABCD is shown in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of the trapezoid?
B) P ≥ 32
From The College Panda ACT Math: Advanced Guide and Workbook (p. 129)¹: Let P denote the perimeter, in inches, of a rectangle with an area of 64 square inches. Which of the following must be true? A) P ≥ 8 B) P ≥ 32 C) P ≥ 64 D) P ≥ 128 E) P ≥ 256
180
From The College Panda ACT Math: Advanced Guide and Workbook (p. 129)¹: The design of a tile consists of five congruent rectangles as shown in the figure below. If the perimeter of each of the rectangles is 30 inches, what is the area, in square inches, of the tile?
48
From The College Panda ACT Math: Advanced Guide and Workbook (p. 129)¹: The total area of the figure shown below is 80 square feet. If the area of rectangle A is four times the area of square B, what is the perimeter, in feet, of the figure?
216
From The College Panda ACT Math: Advanced Guide and Workbook (p. 130)¹: In rhombus CADB below, AB is 24 inches long and CD is 18 inches long. What is the area, in square inches, of CADB?
100
From The College Panda ACT Math: Advanced Guide and Workbook (p. 130)¹: In the figure below, a large square consists of four congruent rectangles and a smaller square. The perimeter of each of the congruent rectangles is 20 inches. What is the area, in square inches, of the large square?
4
From The College Panda ACT Math: Advanced Guide and Workbook (p. 130)¹: The side lengths of the flat, trapezoidal wall of a living room are given in the figure below. James will paint the entire wall with 1 coat of paint, using paint that is sold only in 3-quart containers. Each quart of paint covers an area of 50 square feet with 1 coat of paint. What is the minimum number of containers of paints that James needs to buy?
60
From The College Panda ACT Math: Advanced Guide and Workbook (p. 131)¹: An artist has 30 rectangular strips of cardboard, each a right triangle with dimensions in inches, as shown below. What is the maximum height, in inches, of a rectangular poster 15 inches wide that can be completely covered with these 30 strips of cardboard?
They bisect each other.
What do the two diagonals do to each other in a parallelogram?
A polygon with 4 sides
What is a quadrilateral?
A trapezoid where the nonparallel sides are congruent
What is an isosceles trapezoid?
They are supplementary
What is the relationship between the angles in the following figure?
They are congruent
What is the relationship between the base angles of an isosceles trapezoid?
They are congruent They also bisect each other (because it's a parallelogram)
What is the relationship between the diagonals of a rectangle?
The two pairs of angles are congruent
What is the relationship between the two pairs of opposite angles in a parallelogram?
The two pairs of sides are congruent and parallel
What is the relationship between the two pairs of opposite sides in a parallelogram?
They're supplementary
What is the relationship between two adjacent angles in a parallelogram?
360°
What is the sum of the angles of any quadrilateral?
A parallelogram
What is this shape called?
A rectangle
What is this shape called?
A rhombus
What is this shape called?
A square
What is this shape called?
A trapezoid
What is this shape called?
An isosceles trapezoid
What is this shape called?
A quadrilateral where: 1) Opposite sides are parallel 2) Opposite sides are congruent 3) Opposite angles are congruent 4) Adjacent angles are supplementary 5) Diagonals bisect each other
What's a parallelogram?
A parallelogram with right angles
What's a rectangle?
A parallelogram with four congruent sides
What's a rhombus?
A rectangle with four congruent sides Or a rhombus with right angles
What's a square?
A quadrilateral with one pair of parallel sides
What's a trapezoid?
A = bh where b = Base h = Height NOTE: the base and height MUST be perpendicular to each other!
What's the area of a parallelogram?
A = Lw where L = length w = width
What's the area of a rectangle?
A = (d₁d₂)/2 d₁, d₂ are the diagonals
What's the area of a rhombus?
A = s²
What's the area of a square?
A = 1/2(b₁+b₂)h Where b₁, b₂ = the two bases h = the height
What's the area of a trapezoid?
P = 2(L + w) where L = length w = width
What's the perimeter of a rectangle?
1) They're perpendicular 2) They bisect each other
What's the relationship between the diagonals of a rhombus?
1) They're perpendicular 2) They're congruent 3) They bisect each other
What's the relationship between the diagonals of a square?
64
From The College Panda ACT Math: Advanced Guide and Workbook (p. 124)¹: For trapezoid ABCD shown below, AB = 6, BC = 8, DC = 10. What is the area of the trapezoid?
72
From The College Panda ACT Math: Advanced Guide and Workbook (p. 126)¹: A rectangle has a perimeter of 36. Its width is twice its length. What is the area of the rectangle?
