Example Question - triangular prism
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Finding the Volume of a Triangular Prism
<p>Para calcular el volumen de un prisma triangular, utilizamos la fórmula:</p> <p>V = A_b * h</p> <p>donde A_b es el área de la base y h es la altura del prisma.</p> <p>Primero, calculamos el área de la base triangular:</p> <p>A_b = \frac{1}{2} * base * altura = \frac{1}{2} * 6 \, cm * 8 \, cm = 24 \, cm^2</p> <p>Ahora, usando la altura del prisma (10 cm):</p> <p>V = A_b * h = 24 \, cm^2 * 10 \, cm = 240 \, cm^3</p> <p>El volumen del prisma triangular es 240 cm^3.</p>
Calculating Surface Area of a Triangular Prism
To find the surface area of the triangular prism shown in the image, we can sum the areas of all the individual faces of the prism. The prism has two triangular faces and three rectangular faces. We'll calculate each of these separately and then add them together: 1. The area of one triangular face: Since both triangular faces are identical, we only need to calculate the area for one and then double it. The formula for the area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). Here, the base is 5 cm and the height is 12 cm. Area of one triangle = \( \frac{1}{2} \times 5 \, \text{cm} \times 12 \, \text{cm} = 30 \, \text{cm}^2 \) Since there are two triangles, the total area for the triangular faces: 2 × 30 cm² = 60 cm² 2. The area of the three rectangular faces: We need to consider all three rectangles: the bottom, the side that is parallel to the triangular base, and the back rectangle. - The bottom rectangle has dimensions of 6 cm (length) and 5 cm (width). Area of the bottom rectangle = length × width = 6 cm × 5 cm = 30 cm² - The side rectangle (parallelogram face) has dimensions of 6 cm (base) and 12 cm (slant height). Area of the side rectangle = base × height = 6 cm × 12 cm = 72 cm² - The back rectangle has dimensions of 12 cm (length) and 5 cm (width). Area of the back rectangle = length × width = 12 cm × 5 cm = 60 cm² Adding the area of all three rectangles: 30 cm² + 72 cm² + 60 cm² = 162 cm² Finally, add the areas of the triangles and rectangles together to get the total surface area: Total surface area = area of triangles + area of rectangles Total surface area = 60 cm² (triangles) + 162 cm² (rectangles) Total surface area = 222 cm² So, the surface area of the triangular prism is 222 cm².
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