Plane Geometry - ISEE Lower Level Quantitative Reasoning
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Find the area of the parallelogram:
Find the area of the parallelogram:
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What is the area of the parallelogram ABCD?
What is the area of the parallelogram ABCD?
A parallelogram's area is found by multiplying its height by the base. The height of the parallelogram is not the side. It is the line that makes a right angle with the base. Therefore, the area of this parallelogram is:
A parallelogram's area is found by multiplying its height by the base. The height of the parallelogram is not the side. It is the line that makes a right angle with the base. Therefore, the area of this parallelogram is:
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What is the area of parallelogram ABCD?
What is the area of parallelogram ABCD?
A parallelogram's area is found by multiplying its height by the base. The height of the parallelogram is not the side. It is the line that makes a right angle with the base. Therefore, the area of this parallelogram is:
A parallelogram's area is found by multiplying its height by the base. The height of the parallelogram is not the side. It is the line that makes a right angle with the base. Therefore, the area of this parallelogram is:
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A parallelogram measures 
along its base and is 
high. Calculate the area.
A parallelogram measures
The formula to calucate a parallelogram's area is:
You calculate the parallelogram's area by multiplying its base by its height. Therefore, 
The formula to calucate a parallelogram's area is:
You calculate the parallelogram's area by multiplying its base by its height. Therefore,
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A parallelogram measures 
along its base and is 
high. Calculate the area.
A parallelogram measures
The formula to calucate a parallelogram's area is:
You calculate the parallelogram's area by multiplying its base by its height. Therefore, 
The formula to calucate a parallelogram's area is:
You calculate the parallelogram's area by multiplying its base by its height. Therefore,
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Find the area of a parallelogram whose height is 
and base is 
.
Find the area of a parallelogram whose height is
To solve, simply use the formula for the area of a parallelogram. Thus,
To solve, simply use the formula for the area of a parallelogram. Thus,
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What is the area of a parallelogram if the base is 
, the other side is 
, and the height is 
?
What is the area of a parallelogram if the base is
The area of a parallelogram is 
so the answer would be 
.
The area of a parallelogram is
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Find the area of the given parallelogram:
Find the area of the given parallelogram:
Find the area of the given parallelogram:
To find the area of a parallelogram, simply do the following:
Where b is the base, and h is the height. Note that the height is the length of the perpendicular line connecting both bases. In this case, our height is 12mi and our base is 144 miles.
Find the area of the given parallelogram:
To find the area of a parallelogram, simply do the following:
Where b is the base, and h is the height. Note that the height is the length of the perpendicular line connecting both bases. In this case, our height is 12mi and our base is 144 miles.
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Find the area of the given parallelogram:
Find the area of the given parallelogram:
Find the area of the given parallelogram:
To find the area of a parallelogram, simply use the following formula for area of a parallelogram:
Where b is the base, and h is the height. Note that the height is the length of the perpendicular line connecting both bases. In this case, our height is 12 mi and our base is 144 mi.
Find the area of the given parallelogram:
To find the area of a parallelogram, simply use the following formula for area of a parallelogram:
Where b is the base, and h is the height. Note that the height is the length of the perpendicular line connecting both bases. In this case, our height is 12 mi and our base is 144 mi.
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What is the perimeter of parallelogram ABCD?
What is the perimeter of parallelogram ABCD?
The perimeter of a parallelogram is very easy to find. You just need to add up all the sides. However, you need to notice that the sides "across" from each other are equal on parallelograms. So, your figure could be redrawn:
The perimeter of your figure is therefore:
The perimeter of a parallelogram is very easy to find. You just need to add up all the sides. However, you need to notice that the sides "across" from each other are equal on parallelograms. So, your figure could be redrawn:
The perimeter of your figure is therefore:
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A parallelogram has a side length of 
. It also has a side length of 
. Calculate the perimeter.
A parallelogram has a side length of
A parallelogram has four sides and its opposite sides are equal in length. Therefore, if it has one side length of
, it also has another side length of of 
. Since we know one of its side lenghts is 
, then the remaining side is 
. We can add all 4 side lengths 
to calculate the perimeter.
A parallelogram has four sides and its opposite sides are equal in length. Therefore, if it has one side length of
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What is the perimeter of a parallelogram if the base is 
, the other side is 
, and the height is 
?
What is the perimeter of a parallelogram if the base is
The perimeter of a parallelogram is the sum of all four sides or the sum of two times each side length. The side lengths are 
and 
so the perimeter is 
.
The perimeter of a parallelogram is the sum of all four sides or the sum of two times each side length. The side lengths are
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Find the perimeter of the given parallelogram:
Find the perimeter of the given parallelogram:
Find the perimeter of the given parallelogram:
The perimeter of any shape can be found by adding up the lentghs of its sides.
In this case, we have four sides. 2 that are 16 miles long, and 2 that are 144 miles long.
Find perimeter as follows:
Making our answer 320 miles
Find the perimeter of the given parallelogram:
The perimeter of any shape can be found by adding up the lentghs of its sides.
In this case, we have four sides. 2 that are 16 miles long, and 2 that are 144 miles long.
Find perimeter as follows:
Making our answer 320 miles
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What is the total surface area of the enclosed region?
What is the total surface area of the enclosed region?
First, we must find the missing lengths. Because we know that the length going horizontally across on the bottom is 6 cm and 8 cm, that must mean that the length going across at the top must also equal this sum.
So, the length of the top must equal
6 + 8 =
We are given one value of the length on the top, 4. To find the missing horizontal length on the top, we must subtract 4 from 14.
14 – 4 = 10.
In order to find the other missing length, we must observe that the greatest vertical length of this figure is 12 cm. Because we are given 4 cm and 5 cm, we must subtract 4 and 5 from 12 to find the other missing length.
12 – 4 – 5 =
Now, let's divide this enclosed region in three separate rectangles.
The rectangle at the top has a length of 4 cm and width of 3 cm.
The middle rectangle has a length of
10 + 4 =
14 cm
and a width of 5 cm.
The bottom rectangle has a length of 8 cm and width of 4 cm.
If the formula for the area of a rectangle is length x width, we must now calculate the individual areas of each rectangle and add them up.
Area of top rectangle
4 x 3 = 12cm2
Area of middle rectangle
14 x 5 = 70cm2
Area of bottom rectangle
8 x 4 = 32cm2
12cm2 + 32cm2 + 70cm2 =
114cm2
First, we must find the missing lengths. Because we know that the length going horizontally across on the bottom is 6 cm and 8 cm, that must mean that the length going across at the top must also equal this sum.
So, the length of the top must equal
6 + 8 =
We are given one value of the length on the top, 4. To find the missing horizontal length on the top, we must subtract 4 from 14.
14 – 4 = 10.
In order to find the other missing length, we must observe that the greatest vertical length of this figure is 12 cm. Because we are given 4 cm and 5 cm, we must subtract 4 and 5 from 12 to find the other missing length.
12 – 4 – 5 =
Now, let's divide this enclosed region in three separate rectangles.
The rectangle at the top has a length of 4 cm and width of 3 cm.
The middle rectangle has a length of
10 + 4 =
14 cm
and a width of 5 cm.
The bottom rectangle has a length of 8 cm and width of 4 cm.
If the formula for the area of a rectangle is length x width, we must now calculate the individual areas of each rectangle and add them up.
Area of top rectangle
4 x 3 = 12cm2
Area of middle rectangle
14 x 5 = 70cm2
Area of bottom rectangle
8 x 4 = 32cm2
12cm2 + 32cm2 + 70cm2 =
114cm2
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Robert needs to determine the area of his rectangular wall in order to buy the proper amount of paint at the store. When he measures his wall he determines that it is 12 feet high and 20 feet wide. If one can of paint covers 40 square feet of wall, how many cans of paint does Robert need?
Robert needs to determine the area of his rectangular wall in order to buy the proper amount of paint at the store. When he measures his wall he determines that it is 12 feet high and 20 feet wide. If one can of paint covers 40 square feet of wall, how many cans of paint does Robert need?
Find the area of the wall - 
Divide 
6 cans of paint.
Find the area of the wall -
Divide
6 cans of paint.
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If Bailey is making a quilt for a bed that measures 
feet wide and 
feet long, and she wants there to be an extra foot of quilt to hang over each side of the bed, how much material should she buy.
If Bailey is making a quilt for a bed that measures
In order to determine how much material Bailey needs, we must first find the area of space she needs to cover. Since Bailey would like the quilt to be an extra foot on each side, we must add 
feet to both the length and width.
Width 
Length 
Now we apply the formula for the area of a rectangle, which is 
.
In order to determine how much material Bailey needs, we must first find the area of space she needs to cover. Since Bailey would like the quilt to be an extra foot on each side, we must add
Width
Length
Now we apply the formula for the area of a rectangle, which is
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Mr. Barker is building a rectangular fence. His yard has an area of 24 feet, and the one side of the fence he's already built is 6 feet long.
What is the length of the other side (the width) of the fence?
Mr. Barker is building a rectangular fence. His yard has an area of 24 feet, and the one side of the fence he's already built is 6 feet long.
What is the length of the other side (the width) of the fence?
The answer is 4 feet, because 
and a rectangle must have 4 sides, with 2 sides of one length and 2 sides of another.
feet
making the other side 4 feet,
The answer is 4 feet, because
and a rectangle must have 4 sides, with 2 sides of one length and 2 sides of another.
making the other side 4 feet,
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Give the area of the rectangle in the above diagram.
Give the area of the rectangle in the above diagram.
Multiply the length by the width to get the area of the rectangle:
The area of the rectangle is 198 square inches.
Multiply the length by the width to get the area of the rectangle:
The area of the rectangle is 198 square inches.
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Which could be the dimensions of a rectangle with the area 
?
Which could be the dimensions of a rectangle with the area
To find the area, simply multiply the sides of the rectangle. The only sides which add up to 
are:
To find the area, simply multiply the sides of the rectangle. The only sides which add up to
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Mr. Smith is planting a rectangular garden with a length of 5 ft and a width of 7 ft. What is the area of the garden?
Mr. Smith is planting a rectangular garden with a length of 5 ft and a width of 7 ft. What is the area of the garden?
The area of a rectangle can be calculated by multiplying the length by the width.
The area of a rectangle can be calculated by multiplying the length by the width.
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