LUAS PERMUKAAN GABUNGAN KUBUS DAN LIMAS SEGIEMPAT | MATEMATIKA SD SMP

Summary

In this video, the presenter explains how to calculate the combined surface area of a cube and a square pyramid. The cube’s surface area is adjusted because its top is covered by the pyramid, so only five sides of the cube are considered. For the pyramid, only the four triangular sides are visible, and the area of each triangle is calculated based on its base and height. The video walks through the math step by step, ultimately showing that the total surface area of the combined shapes is 960 cm². Viewers are encouraged to ask questions if needed.

Takeaways

• 😀 The video starts with a greeting and introduction to the lesson on calculating the surface area of a combined cube and square pyramid.
• 😀 The problem involves two shapes: a cube at the bottom and a square pyramid on top, attached to the cube's top face.
• 😀 Only the visible surfaces of both shapes need to be considered for calculating the total surface area.
• 😀 The surface area of the cube is calculated by considering only 5 of its 6 faces since one face is hidden by the pyramid.
• 😀 The formula for the surface area of a cube is 6 × side², but in this case, we only use 5 × side² due to the hidden face.
• 😀 The surface area of the pyramid is calculated by considering the 4 visible triangular faces and excluding the base.
• 😀 The area of each triangular face of the pyramid is calculated using the formula (base × height) / 2.
• 😀 In the example, the side length is given as 12 units, and the height of the triangular faces is 10 units.
• 😀 After calculating the surface area of the cube and the pyramid, the results are added together to find the combined surface area.
• 😀 The final surface area of the combined shapes is 960 cm².

Q & A

What is the main topic discussed in this lesson?

The lesson focuses on calculating the combined surface area of a cube and a square pyramid.

Why is the top face of the cube not considered in the surface area calculation?

The top face of the cube is hidden as it is in contact with the base of the pyramid, so it is not visible and is not included in the surface area calculation.

How do you calculate the surface area of the cube in this scenario?

To calculate the surface area of the cube, you use the formula 5 times the square of the side length (5 * x^2) because one face is hidden, leaving five visible faces.

What is the formula for the surface area of a square pyramid?

For the surface area of the square pyramid, you calculate the area of the four triangular sides. The formula is 4 times the area of one triangle, where each triangle has a base of x and a height of 10.

Why are the four triangular faces of the pyramid important in the surface area calculation?

The four triangular faces are the only visible parts of the pyramid, as the base of the pyramid is hidden inside the cube. The surface area of the pyramid is calculated by adding the areas of these four triangles.

How is the area of a triangular face calculated?

The area of a triangular face is calculated using the formula (base * height) / 2. In this case, the base is 12 (side length of the square), and the height is 10.

What is the total surface area of the cube and pyramid combined?

The combined surface area is the sum of the surface area of the cube (720 cm²) and the surface area of the pyramid's four triangular faces (240 cm²), giving a total of 960 cm².

Why is the surface area of the square pyramid multiplied by 4?

The surface area of the pyramid is multiplied by 4 because there are four identical triangular faces on the pyramid.

How does the side length (x) affect the total surface area?

The side length (x) directly influences the surface area, as both the cube and the pyramid's surface area formulas depend on the value of x. A larger side length results in a larger surface area.

What could be the consequence of not considering the hidden faces in the calculation?

Not accounting for the hidden faces would lead to an overestimation of the surface area, as those faces do not contribute to the visible area of the combined shape.