Geometry - ISEE Lower Level Quantitative Reasoning

Card 0 of 5385

Question

A coordinate plane is shown.

Ralph plotted the following points on the coordinate grid:

Point W (2, 4); Point X (3, 6); Point Y (5, 4); Point Z (6, 6)

A polygon is formed with vertices W, X, Y, and Z. Which type of polygon is formed?

Answer

Begin by plotting the points and connecting the vertices.

The quadrilateral that is created has two sets of parallel sides. Out of the possible answer choices, this can describe both squares and parallelograms. Because the figure does not contain right angles and the sides are not all the same length, it must be a parallelogram.

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Question

A coordinate plane is shown.

Ralph plotted the following points on the coordinate grid:

Point W (1, 1); Point X (7, 3); Point Y (1, 6); Point Z (7, 8)

A polygon is formed with vertices W, X, Y, and Z. Which type of polygon is formed?

Answer

Begin by plotting and connecting the vertices.

The quadrilateral that is created has two sets of parallel sides. Out of the possible answer choices, this can describe both rhombuses and parallelograms. Because the sides are not all the same length, it must be a parallelogram.

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Question

A square has an area of $16\ in^{2}$ . What is the length of one side?

Answer

You can find the area of a square by multiplying two sides together. All of the sides of a square are equal. In this case, $\dpi{100} 4\times 4=16$ , so the length of all of the sides of the square is 4 inches.

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Question

What is the area of a square if one side of the square is 6?

Answer

If one side of a square is 6, then each of the four sides of the square are equal to 6. To find the area of a square, we multiply the length and the height together. The length is 6, and the height is 6, thus the equation we use is .

Remember the formula for the area of a quadrilateral is . For a square, one side is equal to both the length and the width.

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Question

A right triangle has a base of and a height of .

What is the area of the rectangle made by 2 of these triangles aligned along the hypotenuse?

Answer

If one combines the 2 identical triangles, their base and height become the length and width of the rectangle.

Area of a rectangle is:

$length\times height$

In this case

$7\times 4=28$

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Question

If the area of a square is $\small 36 ft^{2}$ , what is the length of each side?

Answer

To find the area of a square, the length must be multiplied by the height. Since a square has four equal sides, the length and width will have the same measurement. We must, therefore, find the square root of $\small 36$ . Since $\small 6\cdot 6=36$ , $\small 6$ is the square root of $\small 36$ , which makes it the measurement for both the length and the width of the square.

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Question

One side of a square is centimeters long. What is the area of the square?

Answer

The formula for finding the area of a square is $area = base\times height$ , or, because this is a square, $area = side^{2}$ .

area = centimeters $\times 4$ centimeters, or $16: cm^{2}$

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Question

James found the area of the square below to be 36 centimeters squared.

What is the length of one side of the square?

Answer

The area of a square can be found by multiplying the length of a side by itself. 36 is equal to 6 times 6, therefore the length of one side is 6 centimeters.

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Question

Michaela drew th square below.

What is the area of the square?

Answer

The area of a square can be found by multiplying the length of a side times itself. The side length of the above square is 12 cm. By finding 12 x 12, we find that the area of the square is 144 cm. squared.

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Question

Daphne found the area of the square below to be 81 centimeters squared.

What is the length of one side of the square?

Answer

The area of a square can be found by multiplying the length of a side by itself. 81 is equal to 9 times 9, therefore the length of one side is 9 centimeters.

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Question

What is the area of a parallelogram with a height of inches and a base of inches?

Answer

The formula for finding the area of a parallelogram is the same as that of finding the area of a rectangle:

$area = base \times height$

In this case, the area equals inches times inches, or $56: in^{2}$ .

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Question

Ted drew the parallelogram shown below.

What is the area of the parallelogram?

Answer

The area of a parallelogram can be found by multiplying the base times the height. The height is the perpendicular distance between two bases. In the above parallelogram, the base is 8 and its height is 4, giving the equation 8 x 4 = A. The area is 32 square feet.

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Question

Wilhelmina drew the parallelogram below.

What is the area of the parallelogram?

Answer

The area of a parallelogram can be found by multiplying the base times the height. The height is the perpendicular distance between two bases. In the above parallelogram, the base is 12 and its height is 6, giving the equation 12 x 6 = A. The area is 72 square millimeters.

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Question

Find the area of the following parallelogram.

Answer

In order to find the area of a parallelogram we use the equation $A=b\times h$

In this case our values are

So, our area is: $A=12\times 10=120$

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Question

Find the area of the following parallelogram.

Answer

The equation for the area of a parallelogram is $A=b\times h$ .

In this case, our values are

so, the area is: $A=8\times4=32$

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Question

What is the length of a rectangular room with an area of and a width of

Answer

$A=l\times w$

We have the area and the width, so we can plug those values into our equation and solve for our unknown.

$56=l\times 7$

$\frac{56}{7}=\frac{l\times 7}{7}$

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Question

What is the length of a rectangular room with an area of and a width of

Answer

$A=l\times w$

We have the area and the width, so we can plug those values into our equation and solve for our unknown.

$80=l\times 8$

$\frac{80}{8}=\frac{l\times 8}{8}$

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Question

What is the length of a rectangular room with an area of and a width of

Answer

$A=l\times w$

We have the area and the width, so we can plug those values into our equation and solve for our unknown.

$100=l\times 5$

$\frac{100}{5}=\frac{l\times 5}{5}$

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Question

What is the length of a rectangular room with an area of and a width of

Answer

$A=l\times w$

We have the area and the width, so we can plug those values into our equation and solve for our unknown.

$120=l\times 10$

$\frac{120}{10}=\frac{l\times 10}{10}$

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Question

What is the length of a rectangular room with an area of and a width of

Answer

$A=l\times w$

We have the area and the width, so we can plug those values into our equation and solve for our unknown.

$48=l\times 8$

$\frac{48}{8}=\frac{l\times 8}{8}$

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