Question

1. look at the figure.

what is the area of the figure?
a. 24 square units
b. 27 square units
c. 36 square units
d. 54 square units

1. look at the picture of the flashlight.

which of these is the best estimate of the length of the
a. 0 feet
b. 90 meters
c. 0 inches

Explanation:

Question 1

Step1: Split the figure

The figure can be split into two rectangles. One is a \(3\times3\) square (or rectangle) and the other is a \(9\times3\) rectangle? Wait, no, better to split into a \(3\times6\) and a \((9 - 3)\times3\)? Wait, no, looking at the dimensions: the total height is 6, with a notch of 3 (so the top part is 3x3, and the bottom part is 9x3? Wait, no, let's re - examine. The vertical side is 6, horizontal is 9. The upper left is a square of 3x3, and the remaining part: the horizontal length for the lower rectangle is 9, vertical height is 3, and the upper square is 3x3. Wait, actually, another way: the area can be calculated as the area of a \(6\times9\) rectangle minus the area of a \(3\times(9 - 3)\) rectangle? No, wait, the figure is like a big rectangle with a smaller square cut out? Wait, no, the given figure: the left side is 6, bottom is 9, top left has a square of 3x3, and the right part has height 3. So we can split it into two rectangles: one is \(3\times6\) (left part) and the other is \((9 - 3)\times3=(6)\times3\). Wait, no, \(3\times6 = 18\), \(6\times3=18\), total \(18 + 18=36\)? Wait, no, wait the first rectangle: the left rectangle has width 3 and height 6, area \(3\times6 = 18\). The right rectangle has width \(9 - 3=6\) and height 3, area \(6\times3 = 18\). Total area \(18+18 = 36\)? Wait, but let's check the options. Option C is 36 square units. Wait, but maybe my splitting is wrong. Alternatively, the figure can be seen as a \(9\times3\) rectangle plus a \(3\times3\) square. \(9\times3=27\), \(3\times3 = 9\), total \(27 + 9=36\). Yes, that's correct. So the area is 36 square units.

Step2: Calculate areas

First rectangle: length = 9, width = 3, area \(A_1=9\times3 = 27\). Second rectangle (square): length = 3, width = 3, area \(A_2 = 3\times3=9\). Total area \(A=A_1+A_2=27 + 9=36\) square units.

We need to estimate the length of a flashlight. Let's analyze the options:

• Option A: 9 feet is too long for a flashlight (a foot is about 30 cm, 9 feet is about 2.7 meters, which is way too long for a flashlight).
• Option B: 90 meters is extremely long (a meter is about 3 feet, 90 meters is about 270 feet, which is impossible for a flashlight).
• Option C: 9 inches is a reasonable length for a flashlight (an inch is about 2.54 cm, 9 inches is about 22.86 cm, which is a typical length for a flashlight). Wait, but the option C is "9 inches" (assuming the option C is 9 inches, as the text shows "C. 9 inches").

Answer:

C. 36 square units

Question 2