Latihan Matematika Pts Kelas 8 Semester 2

Explanation
The surface area of a prism consists of the sum of the areas of all its faces. In this case, the base of the prism is a square with an area of 36 cm^2. Since a square has all sides equal, we can find the length of one side by taking the square root of the area, which is 6 cm. The surface area of the four sides of the prism is equal to the perimeter of the base multiplied by the height, which is 4 times the side length (4 * 6 cm) multiplied by the height of 20 cm, resulting in 480 cm^2. Adding the area of the two bases (2 * 36 cm^2), the total surface area of the prism is 552 cm^2.

Explanation
The correct answer is 154 cm2. This is because the area that is shaded in the given figure is a square with side length 7 cm. The formula for finding the area of a square is side length squared, so the area of this square is 7 cm * 7 cm = 49 cm2. Since there are 4 smaller squares within the larger square, the shaded area is 4 * 49 cm2 = 196 cm2. However, only half of each smaller square is shaded, so the final shaded area is 196 cm2 / 2 = 98 cm2. Therefore, the correct answer is 154 cm2.

Explanation
The correct answer is 125. The total surface area of a cube is given by 6 times the square of its side length. If the total surface area is 150 cm2, then the side length can be found by taking the square root of 150/6, which is approximately 3.536 cm. The volume of a cube is given by the cube of its side length. Therefore, the volume of the cube is approximately 3.536^3 = 125 cm3.

Explanation
In the given image, angle ABC is the largest angle among all the angles mentioned in the options. Therefore, the correct answer is 80°.

Explanation
The length of the hypotenuse in a right-angled triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the given lengths of the two sides are 16 cm and x cm. Plugging these values into the Pythagorean theorem, we get 16^2 + x^2 = 34^2. Simplifying this equation, we find that x^2 = 1156 - 256 = 900. Taking the square root of both sides, we get x = 30. Therefore, the value of x is 30 cm.

Explanation
The volume of a prism can be calculated by multiplying the area of the base by the height. In this case, the base of the prism is a rhombus with diagonals measuring 16 cm and 20 cm. The area of a rhombus can be calculated by multiplying the lengths of the diagonals and dividing by 2. So, the area of the base is (16 cm * 20 cm) / 2 = 160 cm². Multiplying this by the height of 24 cm gives us a volume of 3,840 cm³.

Explanation
The correct answer is 30 cm² because the question asks for the area of the triangle, and 30 cm² is the only option that represents an area measurement.

Explanation
The volume of a trapezoidal prism can be calculated by multiplying the area of the trapezoid base by the height of the prism. In this case, the length of the parallel sides of the trapezoid base are given as 18 cm and 12 cm, and the distance between them is given as 10 cm. To find the area of the trapezoid, we can use the formula (a+b)/2 * h, where a and b are the lengths of the parallel sides and h is the distance between them. Plugging in the given values, we get (18+12)/2 * 10 = 150 cm^2. Finally, multiplying the area by the height of the prism (20 cm), we get 150 cm^2 * 20 cm = 3000 cm^3, which is the volume of the prism.

Explanation
The area of a sector of a circle can be calculated using the formula A = (θ/360) * π * r^2, where θ is the central angle and r is the radius of the circle. In this case, the central angle is not given, so we cannot directly calculate the area of the sector. Therefore, an explanation for the given correct answer is not available.

Explanation
The length and width of a rectangle are in a ratio of 4:3. If the area is 48 cm2, we can find the length and width by finding the factors of 48 that are in a 4:3 ratio. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors that are in a 4:3 ratio are 12 and 16. So, the length is 12 cm and the width is 16 cm. To find the diagonal, we can use the Pythagorean theorem: diagonal^2 = length^2 + width^2. Plugging in the values, we get diagonal^2 = 12^2 + 16^2 = 144 + 256 = 400. Taking the square root of both sides, we get diagonal = 20 cm. Therefore, the correct answer is 20 cm.

Explanation
The given shape consists of a rectangular prism (balok) and a pyramid (limas). To find the volume, we need to calculate the volume of each shape separately and then add them together. The volume of the rectangular prism can be found by multiplying its length, width, and height. The volume of the pyramid can be found by multiplying the base area (length times width) with the height and dividing it by 3. By calculating the volumes of both shapes and adding them together, we get a volume of 1,800 cm3.

Explanation
The length of the tangent line to the external intersection of two circles is equal to the difference of the radii of the circles. In this case, the larger circle has a radius of 8 cm and the smaller circle has a radius of 2 cm. Therefore, the length of the tangent line is 8 cm - 2 cm = 6 cm.

Explanation
The length of the diagonal of a square can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of each side of the square is 8 cm. By substituting the values into the Pythagorean theorem, the length of the diagonal is found to be 8√2.

Explanation
The total cost of painting the inner walls of the rectangular hall can be calculated by finding the surface area of the walls and multiplying it by the cost per square meter. The surface area of the walls can be found by adding the areas of all four walls. The area of each wall can be calculated by multiplying the length of the wall by its height. In this case, the length is 9 meters, the width is 6 meters, and the height is 5 meters. Therefore, the total cost of painting the walls is (2 * 9 * 5 + 2 * 6 * 5) * 50,000 = 7,500,000.