Question

26 a cartesian plane is shown.
select the correct statement below.
o is located where \\(x = 0\\) and \\(y < 0\\).
j is located where \\(x > 0\\) and \\(y < 0\\).
k is located where \\(x < 0\\) and \\(y > 0\\).
l is located where \\(x < 0\\) and \\(y = 0\\).

27 the louvre pyramid in paris, france, is made up of four triangles and a square.
roland is hired to clean the interior sides and the floor of the louvre pyramid.
what is the area that roland will need to clean?
\\(\text{m}^2\\)

Explanation:

Analyze Question 26

We need to determine the correct statement regarding the points plotted on the Cartesian plane.

• Point \(O\) is at the origin, where \(x = 0\) and \(y = 0\).
• Point \(J\) is in Quadrant IV, where \(x > 0\) and \(y < 0\).
• Point \(K\) is in Quadrant I, where \(x > 0\) and \(y > 0\).
• Point \(L\) is on the negative x-axis, where \(x < 0\) and \(y = 0\).

Let's evaluate the given choices:

• "O is located where \(x = 0\) and \(y < 0\)." (Incorrect, \(O\) is at the origin where \(y = 0\))
• "J is located where \(x > 0\) and \(y < 0\)." (Correct, \(J\) is in Quadrant IV)
• "K is located where \(x < 0\) and \(y > 0\)." (Incorrect, \(K\) is in Quadrant I where \(x > 0\))
• "L is located where \(x < 0\) and \(y = 0\)." (Correct, \(L\) is on the negative x-axis. Wait, let's look closely at the options in the image:
• Option 1: O is located where \(x = 0\) and \(y < 0\).
• Option 2: J is located where \(x > 0\) and \(y < 0\).
• Option 3: K is located where \(x < 0\) and \(y > 0\).
• Option 4: L is located where \(x < 0\) and \(y = 0\).

Both Option 2 and Option 4 describe their respective points correctly. Let's re-verify the position of \(L\). Point \(L\) is on the negative x-axis, so \(x < 0\) and \(y = 0\). Point \(J\) is in Quadrant IV, so \(x > 0\) and \(y < 0\). Both statements are mathematically true. However, looking closely at the diagram, \(L\) is clearly on the horizontal axis to the left of the origin, making \(x < 0, y = 0\) extremely precise. Let's provide the correct options for the multiple-choice format.)

Calculate the area for Question 27

Using the Geometric Formulas knowledge point, we need to find the total surface area that Roland needs to clean.

• The Louvre Pyramid has a square base and four triangular sides.
• Roland is hired to clean the "interior sides and the floor" of the pyramid. This means we need to find the total surface area of the pyramid, which is the sum of the area of the square base (the floor) and the areas of the four triangular faces (the sides).
• Base of the square: \(s = 35\text{ m}\).
• Slant height of the triangular faces: \(h_s = 28.6\text{ m}\).

Calculate the area of the square base

Using the Geometric Formulas knowledge point for the area of a square:

$$ \text{Area}_{\text{base}} = s^2 = 35^2 = 1225\text{ m}^2 $$

Calculate the area of the four triangular faces

Using the Geometric Formulas knowledge point for the area of a triangle:

$$ \text{Area}_{\text{one triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 35 \times 28.6 = 500.5\text{ m}^2 $$

Since there are four identical triangular faces:

$$ \text{Area}_{\text{four triangles}} = 4 \times 500.5 = 2002\text{ m}^2 $$

Calculate the total area to clean

Sum the base area and the lateral area:

$$ \text{Total Area} = \text{Area}_{\text{base}} + \text{Area}_{\text{four triangles}} = 1225 + 2002 = 3227\text{ m}^2 $$

Answer:

Question 26

• O is located where \(x = 0\) and \(y < 0\).
• J is located where \(x > 0\) and \(y < 0\). (Correct answer)
• K is located where \(x < 0\) and \(y > 0\).
• L is located where \(x < 0\) and \(y = 0\). (Correct answer)

Question 27

\(3227\)