Example Question - dimensions
Here are examples of questions we've helped users solve.
Calculating Dimensions in a Geometric Figure
<p>To calculate the missing dimensions in the geometric figure, we use the given measurements and understand that opposite sides of a rectangle are equal in length.</p> <p>The bottom horizontal length marked as $x$ must be equal to the top horizontal length, which is $3+14+6 = 23$ units. Therefore, $x = 23$ units.</p> <p>The vertical length on the right, also marked as $y$, should be equal to the left vertical length, which is $1+17+1= 19$ units. Therefore, $y = 19$ units.</p> <p>Therefore, the missing dimensions are $x = 23$ units and $y = 19$ units.</p>
Calculating the Volume of a Rectangular Prism
The image displays a rectangular prism (also known as a rectangular solid or a cuboid) with labeled dimensions. The dimensions given are 13 cm for the length, 5 cm for the width (or depth), and 6 cm for the height. If the question from the image is to find the volume of the rectangular prism, the formula to use is: Volume = length × width × height Applying the given dimensions to this formula: Volume = 13 cm × 5 cm × 6 cm Volume = 65 cm² × 6 cm Volume = 390 cm³ The volume of the rectangular prism is 390 cubic centimeters.
Solving Area Problems with Mixed Numbers
The image shows two mixed numbers: 4 and 5/6 feet by 2 and 1/3 feet. To solve problems like these, typically involving the dimensions of an area, you multiply the length by the width. First, convert each mixed number to an improper fraction: \[ 4 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6} \] \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \] Now multiply the two improper fractions together: \[ \frac{29}{6} \times \frac{7}{3} = \frac{29 \times 7}{6 \times 3} \] \[ = \frac{203}{18} \] Now we will convert this improper fraction back to a mixed number and simplify if necessary: \[ \frac{203}{18} = 11 \frac{7}{18} \] (11 is the whole number part, because 203 divided by 18 is 11 with a remainder of 7.) So, the area covered is 11 and 7/18 square feet.
Calculating Area of L-Shaped Polygon
The image displays an L-shaped polygon with dimensions given in units. To find the area of the polygon, we would typically divide the shape into smaller, more manageable rectangles or squares, calculate the area of each, and then combine these areas. However, in this case, it's simpler to subtract the area of the missing rectangle from the area of the larger rectangle that would encompass the entire L-shape. So first, let’s find the outer rectangle’s dimensions if the L-shape was closed to form a rectangle. The width of the rectangle would be 15 units (as given), and the length would be 7 + 7 = 14 units. Now calculate the outer rectangle’s area: 15 units * 14 units = 210 square units. Next, subtract the area of the missing bottom-right rectangle, which has dimensions of 13 units by 7 units: 13 * 7 = 91 square units. Finally, subtract the area of the smaller rectangle from the area of the larger rectangle: 210 square units - 91 square units = 119 square units. So, the area of the L-shaped polygon is 119 square units.
Solving Area of Rectangles Inside Each Other
The image shows two rectangles, one inside the other. The larger rectangle has a length described as "x + 8" and a width described as "x + 5". The smaller rectangle, presumably positioned inside the larger one, has a length described as "x + 1" and a width described as "x". To solve a question involving these rectangles, we would typically be asked to express the area of one in terms of the other or find the dimensions of the rectangles given certain conditions. However, since the specific question isn't stated in the image, I'll provide a general approach. If we were to find the area of each rectangle, we would: 1. Calculate the area of the larger rectangle by multiplying its length and width: Area = (x + 8)(x + 5) 2. Calculate the area of the smaller rectangle by multiplying its length and width: Area = (x + 1)(x) Without additional information or a specific question, we cannot solve further. If you have a particular equation or condition that relates these rectangles, please provide that for further assistance.
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