Question

Use the image to answer the question.

A composite shape is drawn using a rectangle and a triangle. The rectangle has a base labeled as 6 centimeters. A triangle showing a perpendicular height of 6 centimeters is stacked on the top side of the rectangle. The base of the triangle and the top of the rectangle have a common side. Right angle symbols are shown on all four corners of the rectangle.

John Roy creates this drawing of a composite shape for an art contest. The area of the drawing is 78 square centimeters. What is the height of the rectangle?

(1 point)
Responses

13 centimeters
13 centimeters

12 centimeters
12 centimeters

8 centimeters
8 centimeters

10 centimeters
10 centimeters
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Question
Use the image to answer the question.

A horizontally aligned rectangle is shown as 10 meters long and 6 meters wide. A rectangular area is removed from the bottom right corner, with the remaining length as 8 meters and remaining width as 4 meters. Right angle marks are shown in the five corners of the composite shape.

Rebekah designs a playing field for a new sport. The playing field is pictured. What is the area of the playing field?

(1 point)
Responses

60 square meters
60 square meters

32 square meters
32 square meters

56 square meters
56 square meters

58 square meters
58 square meters
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Answer 1

First problem:
Rectangle area = 6·h. Triangle area = 1/2·6·6 = 18. So 6h + 18 = 78 → 6h = 60 → h = 10 cm.

Second problem:
Full rectangle area = 10·6 = 60 m². The removed corner is (10−8) by (6−4) = 2·2 = 4 m². Remaining area = 60 − 4 = 56 m².

Answers: 10 centimeters; 56 square meters.