Example Question - composite figure
Here are examples of questions we've helped users solve.
Perimeter of a Composite Figure
<p>El perímetro \( P \) de la figura compuesta se puede calcular sumando las longitudes de todos los lados exteriores de la figura.</p> <p>La figura está compuesta por dos rectángulos que comparten un lado. Para evitar contar este lado compartido dos veces, calcularemos el perímetro como si fuera un rectángulo grande.</p> <p>El lado largo del rectángulo grande es \( x + x + 4 \).</p> <p>El lado corto del rectángulo grande (que se muestra en la imagen) es \( x \).</p> <p>El perímetro total es por lo tanto \( P = 2 \cdot (x + x + 4) + 2 \cdot x \).</p> <p>Simplificando, \( P = 2 \cdot (2x + 4) + 2x \).</p> <p>Entonces, \( P = 4x + 8 + 2x \).</p> <p>Finalmente, \( P = 6x + 8 \).</p>
Calculating Surface Area of a Composite Figure
To calculate the surface area of this composite figure, we should break it down into its component rectangles and calculate the area of each, making sure not to count any hidden surfaces. First, let's consider the larger cuboid on the left: - It has two sides that are 16 in. by 8 in. - It has two sides that are 16 in. by 8 in. (top and bottom). - It has two sides that are 16 in. by 8 in. (front and back). Next, we consider the smaller cuboid on the right: - It has two sides that are 8 in. by 6 in. (left and right side, but the left side overlaps with the larger cuboid, so we only consider the right side). - It has a top side that is 8 in. by 6 in. - It has a front side that is 6 in. by 8 in. - It does not have a visible back side because it is covered by the larger cuboid. - It has a bottom side that is 8 in. by 6 in. Now, we will calculate the areas of all the visible sides and sum them up: Larger cuboid: - 2 sides (front and back): 2 * (16 in * 8 in) = 256 in² * 2 = 512 in² - 2 sides (left and right): 2 * (16 in * 8 in) = 256 in² * 2 = 512 in² - But we need to subtract the area where the smaller cuboid overlaps which is 6 in * 8 in = 48 in² Smaller cuboid: - 1 side (right side): 8 in * 6 in = 48 in² - 1 top side: 8 in * 6 in = 48 in² - 1 front side: 8 in * 6 in = 48 in² - Bottom side (but it is fully overlapping with the larger cuboid, so it's not added to the surface area) Adding all the calculated areas: Total surface area = (512 in² + 512 in² - 48 in²) + (48 in² + 48 in² + 48 in²) Total surface area = 1024 in² - 48 in² + 144 in² Total surface area = 1120 in² So, the surface area of the figure is 1120 square inches.
Calculating Volume of Composite 3D Figure
To find the volume of the composite figure in the image, consider it as two separate rectangular prisms and then add their volumes together. **First rectangular prism:** The dimensions of the larger prism include the entire length, width, and height of the figure. - Length (l₁) = 9.1 cm - Width (w₁) = 2.4 cm + 4.7 cm + 2.4 cm - Height (h₁) = 2.4 cm Calculate the volume (V₁) of the first prism: V₁ = l₁ × w₁ × h₁ V₁ = 9.1 cm × (2.4 cm + 4.7 cm + 2.4 cm) × 2.4 cm V₁ = 9.1 cm × 9.5 cm × 2.4 cm V₁ = 9.1 cm × 22.8 cm V₁ = 207.48 cm³ **Second rectangular prism (the cut-out section):** The dimensions of the cut-out are given inside the larger prism. - Length (l₂) = 4.7 cm - Width (w₂) = 2.4 cm - Height (h₂) = 2.4 cm Calculate the volume (V₂) of the cut-out section: V₂ = l₂ × w₂ × h₂ V₂ = 4.7 cm × 2.4 cm × 2.4 cm V₂ = 11.328 cm³ Now subtract V₂ from V₁ to get the total volume (V) of the composite figure: V = V₁ - V₂ V = 207.48 cm³ - 11.328 cm³ V ≈ 196.152 cm³ Round to the nearest hundredth, if necessary: V ≈ 196.15 cm³ So, the volume of the composite figure is approximately 196.15 cubic centimeters.
Calculating Area of Composite Figure Using Rectangles
To find the area of the composite figure shown in the image, we can divide it into simpler shapes (such as rectangles) and then calculate the area of each before summing them up. From the image, it appears that we can divide the figure into two rectangles: 1. The larger rectangle on the left, which has a width of 3 cm (since the entire bottom length is 8 cm, and the length to the right is 5 cm, the difference is 8 cm - 5 cm = 3 cm) and a height of 6 cm. 2. The smaller rectangle on the right, which has a width of 5 cm and a height of 2 cm (since the entire length on the left is 6 cm, and the topmost length is 4 cm, the difference is 6 cm - 4 cm = 2 cm). Let's calculate their areas: For the larger rectangle: Area = width × height = 3 cm × 6 cm = 18 cm² For the smaller rectangle: Area = width × height = 5 cm × 2 cm = 10 cm² Now, we add the areas of the two rectangles together to get the total area of the figure: Total Area = Area of larger rectangle + Area of smaller rectangle Total Area = 18 cm² + 10 cm² = 28 cm² So, the area of the figure is 28 square centimeters.
Calculating Area of Composite Figure with Rectangles
To find the area of this composite figure, which is a combination of rectangles, we can approach it by breaking down the shape into simpler parts that we can easily calculate the area for and then combine them. From the image, we can see that there is a large rectangle on the right side of the figure with the dimensions of 5 cm by 8 cm. Next to it on the left, there is an upside-down "L" shaped figure which can be broken down into two smaller rectangles - one with the dimensions of 3 cm by 3 cm and the other 2 cm by 5 cm. Let's calculate the area for each part: 1. Large rectangle: 5 cm x 8 cm = 40 cm² 2. Small square (3 cm by 3 cm): 3 cm x 3 cm = 9 cm² 3. Small rectangle (2 cm by 5 cm): 2 cm x 5 cm = 10 cm² Now let's add up the areas of all parts: Total area = Large rectangle area + Small square area + Small rectangle area Total area = 40 cm² + 9 cm² + 10 cm² Total area = 59 cm² So, the area of the figure is 59 square centimeters.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com