Area of Special Quadrilaterals Quick Check

2 of 52 of 5 Items

Question
Use the image to answer the question.

An illustration shows a trapezoid with parallel sides on the left and right. The left side is 10 inches and right side is 16 inches. The top slanting side is labeled 7 inches. Two perpendicular dotted lines of 6 inches each are drawn from the top and bottom left vertices to the right side.

What is the area of the quadrilateral?

(1 point)
Responses

91 in.2
91 in. squared

39 in.2
39 in. squared

78 in.2
78 in. squared

96 in.2
96 in. squared

11 answers

The correct answer is:

78 in.²
Area of Special Quadrilaterals Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.

An illustration shows a trapezoid with top side as 4 centimeters, and the left as the longest side of 9 centimeters. The opposite parallel side on the right is 6 centimeters. A diagonal bottom side is 5 centimeters. The top side is perpendicular to the left and right sides as denoted by right two angle symbols. A perpendicular dotted line from the bottom right vertex to the left side is drawn. The dotted line makes one right angle symbol with right side and two right angle symbols with the left side. It forms a right triangle at the bottom of the trapezoid, with the 5 centimeter side as the hypotenuse.

Find the area of the quadrilateral.

(1 point)
Responses

54 cm2
54 cm squared

60 cm2
60 cm squared

24 cm2
24 cm squared

30 cm2
To find the area of the trapezoid, we need to calculate the height first. The height can be calculated using Pythagorean theorem in the right triangle formed by the dotted line, 6 cm side and 5 cm side:
Height = √(5^2 - 3^2) = √(25 - 9) = √16 = 4 cm

Now, we can calculate the area:
Area = 1/2 * (sum of parallel sides) * height
Area = 1/2 * (9 + 6) * 4 = 1/2 * 15 * 4 = 30 cm²

So, the correct answer is:
30 cm²
Use the image to answer the question.

An illustration shows a trapezoid with parallel sides on the top and bottom. The top side is 24 centimeters and bottom side is 20 centimeters. Two perpendicular dotted lines of 10 centimeters are drawn from the bottom vertices to the top side. The two perpendicular lines are denoted by 4 right angle symbols.

What is the area of the quadrilateral?

(1 point)
Responses

220 cm2
220 cm squared

240 cm2
240 cm squared

480 cm2
480 cm squared

460 cm2
To find the area of the trapezoid, we need to first calculate the height. The height can be calculated by subtracting the difference of the top and bottom side lengths divided by 2 from the length of the perpendicular dotted line:

Height = 10 - ((24 - 20) / 2) = 10 - (4 / 2) = 10 - 2 = 8 cm

Now we can calculate the area:

Area = 1/2 * (sum of parallel sides) * height
Area = 1/2 * (24 + 20) * 8
Area = 1/2 * 44 * 8
Area = 22 * 8
Area = 176 cm²

Therefore, the area of the trapezoid is 176 cm².
use the answers i gave you
Apologies for the oversight. Based on your provided responses, the answer would be:

240 cm²

Therefore, the area of the quadrilateral is 240 cm².
Area of Special Quadrilaterals Quick Check
4 of 54 of 5 Items

Question
Use the image to answer the question.

An illustration shows a parallelogram. The top side, slanted downward, is 10 inches. The left side is 14 inches. A dotted perpendicular line is drawn from top right vertex to the left side and labeled as 8 inches. It is denoted by one right angle symbol on the right and two right angle symbols on the left.

What is the area of the quadrilateral?

(1 point)
Responses

112 in.2
112 in. squared

140 in.2
140 in. squared

80 in.2
80 in. squared

102 in.2
To find the area of the parallelogram, we need to calculate the height of the parallelogram. The height can be determined by the perpendicular line drawn from the top right vertex to the left side.

Given:
Top side (slanted) = 10 inches
Left side = 14 inches
Perpendicular line = 8 inches

Since the opposite sides of a parallelogram are equal in length, the opposite side to the left side will also be 8 inches. This creates a right-angled triangle with the perpendicular line as the hypotenuse. Using the Pythagorean theorem:
Height = √(8^2 - 6^2) = √(64 - 36) = √28 = 2√7 inches

Now, we can calculate the area:
Area = Base x Height
Area = 14 inches x 2√7 inches = 28√7 in²

Therefore, the correct answer would be:
140 in.²
Area of Special Quadrilaterals Quick Check
5 of 55 of 5 Items

Question
Use the image to answer the question.

An illustration shows a parallelogram. The top side, slanting downward, is 5 centimeters, and the right side is 25 centimeters. A dotted perpendicular line is drawn from top right vertex to the left side and is labeled as 4 centimeters. It is denoted by two right angle symbols formed with the two sides.

What is the area of the quadrilateral?

(1 point)
Responses

80 cm2
80 cm squared

100 cm2
100 cm squared

125 cm2
125 cm squared

75 cm2
75 cm squared
To find the area of the parallelogram, we need to find the height first. The height can be calculated using the perpendicular dotted line as one of the sides of a right triangle with the other sides being the top side and the slant height.

Given:
Top side (slanting) = 5 centimeters
Right side = 25 centimeters
Perpendicular line = 4 centimeters

Using the Pythagorean theorem:
Height = √(5^2 - 3^2) = √(25 - 16) = √9 = 3 cm

Now, we can calculate the area:
Area = Base x Height
Area = 25 cm x 3 cm = 75 cm²

Therefore, the correct answer is:
75 cm²