Rectangles - ISEE Middle Level Quantitative Reasoning

Card 0 of 1120

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=3\times 3$ $A=2\times 1$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=6\times 8$ $A=7\times 5$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to split the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 5$ $A=6\times 4$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=6\times 2$ $A=5\times 2$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 2$ $A=6\times 3$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=9\times 8$ $A=8\times 3$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=4\times 6$ $A=4\times 2$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=5\times 5$ $A=3\times 3$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=4\times 2$ $A=9\times 4$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=3\times 3$ $A=11\times 2$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=8\times 5$ $A=6\times 4$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=2\times 12$ $A=2\times 2$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

What is the area of the figure below?

Answer

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=2\times 4$ $A=4\times 1$

To find our final answer, we need to add the areas together.

Compare your answer with the correct one above

Question

Using the information given in each question, compare the quantity in Column A to the quantity in Column B.

A certain rectangle is seven times as long as it is wide.

Column A Column B

the rectangle's the rectangle's

perimeter area

(in units) (in square units)

Answer

This type of problem reminds us to be wary of simply plugging in numbers (which works with certain problems). If you were to choose 1 and 7 here, the perimeter would be larger; if you chose 10 and 70, the area would be much larger.

To solve this problem with variables:

$area=w\cdot (7w)= 7w^{2}$

From here we can see that smaller values of will lead to a larger perimeter, while larger values of will lead to a larger area.

The answer cannot be determined.

Compare your answer with the correct one above

Question

If the length of a rectangle is twice the width, and the width is three inches, what is the area of the rectangle?

Answer

In order to find the area of a rectangle we use the formula $\small A=l\cdot w$ .

In this problem, we know the width is $\small 3: in$ . We also know that the length is twice as long as the width, which can be written as $\small 2w$ . This means that in order to find the length, we must multiply the width by $\small 2$ .

$\small 2(3: in)=6: in$

Now that we know that our length is $\small 6: in$ , we simply multiply it by our width of $\small 3: in$ .

$\small \small 6: in\cdot 3: in=18: in^{2}$

The area of the rectangle is $\small 18: in^{2}$ .

Compare your answer with the correct one above

Question

Which is the greater quantity?

(a) The surface area of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The surface area of a cube with sidelength 300 millimeters

Answer

(a) The surface of a rectangular prism comprises six rectangles, so we can take the sum of their areas.

Two rectangles have area: $60 \times 30 = 1,800 \textrm{ cm}^{2}$ .

Two rectangles have area: $60 \times 15 = 900 \textrm{ cm}^{2}$ .

Two rectangles have area: $15 \times 30 = 450 \textrm{ cm}^{2}$ .

Add the areas: $A = 1,800 + 1,800 + 900 + 900 + 450 + 450 = 6,300 \textrm{ cm}^{2}$

(b) The surface of a cube comprises six squares, so we can square the sidelength - which we rewrite as 30 centimeters - and multiply the result by 6:

$A = 6 \times 30 ^{2} = 6 \times 900 = 5,400 \textrm{ cm}^{2}$ .

The first figure has the greater surface area.

Compare your answer with the correct one above

Question

Column A Column B

The area of a The area of a square

rectangle with sides with sides 7cm.

11 cm and 5 cm.

Answer

First, you must calculate Column A. The formula for the area of a rectangle is . Plug in the values given to get $11\cdot 5$ , which gives you . Then, calculate the area of the square. Since all of the sides of a square are equal, the formula is , or . Therefore, the area of the square is $7\cdot 7$ , which gives you . Therefore, the quantity in Column A is greater.

Compare your answer with the correct one above

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.

$56=l\times 7$

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

Compare your answer with the correct one above

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.

$80=l\times 8$

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

Compare your answer with the correct one above

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.

$100=l\times 5$

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

Compare your answer with the correct one above

Tap the card to reveal the answer