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ISEE Middle Level Math : Plane Geometry

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Example Question #214 : Geometry

A trapezoid has a height of inches and bases measuring inches and inches. What is its area?

Possible Answers:

$1,500\; \textrm{in}^{2}$

$900\; \textrm{in}^{2}$

$864\; \textrm{in}^{2}$

$600\; \textrm{in}^{2}$

$750\; \textrm{in}^{2}$

Correct answer:

$750\; \textrm{in}^{2}$

Explanation:

Use the following formula, with B = 36,b = 24,h=25 :

$A = \frac{1}{2} (B+b)h = \frac{1}{2} (36+24) \cdot 25 = 750$

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Example Question #1 : How To Find The Area Of A Trapezoid

Find the area of a trapezoid with bases equal to 7 and 9 and height is 2.

Possible Answers:

126

Correct answer:

Explanation:

To solve, simply use the formula for the area of a trapezoid.

b1=7, b2=9, h=2

Thus,

$A=\frac{1}{2}(b1+b2)h=\frac{1}{2}(7+9)(2)=16$

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Example Question #2 : How To Find The Area Of A Trapezoid

Find the area of a trapezoid with bases of 10 centimeters and 8 centimeters, and a height of 4 centimeters.

Possible Answers:

$72cm^{2}$

$36cm^{2}$

$112cm^{2}$

$56cm^{2}$

Correct answer:

$36cm^{2}$

Explanation:

The formula for area of a trapezoid is:

$A=\frac{1}{2} (b_{1}+b_{2}) \times h$

where

b_1=10, b_2=8, h=4

therefore the area equation becomes,

$A = \frac{1}{2} (10 + 8) \times 4$

$A = \frac{1}{2} (72)$

$A = 36cm^{2}$

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Example Question #3 : How To Find The Area Of A Trapezoid

You recently bought a new bookshelf with a base in the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the depth is 8 inches, what is the area of the base of your new bookshelf?

Possible Answers:

Cannot be determined from the information provided.

$\frac{5}{2}ft^2$

$\frac{3}{5}ft^2$

$\frac{5}{3}ft^2$

Correct answer:

$\frac{5}{3}ft^2$

Explanation:

To find the area of a trapezoid, we need to use the following formula:

$A_{trapezoid}=\frac{a+b}{2}*h$

Where a and b are the lengths of the bases, and h is the perpendicular distance from one base to another.

We are given a and b, and then h will be the same as our depth. The tricky part is realizing that our depth is in inches, while our base lengths are in feet. We need to convert 8 inches to feet:

$8in*\frac{1ft}{12in}=\frac{8}{12}=\frac{2}{3}ft$

Next, plug it all into our equation up above.

$A_{trapezoid}=\frac{2+3}{2}*\frac{2}{3}=\frac{5}{2}*\frac{2}{3}$

$\frac{5}{2}*\frac{2}{3}=\frac{5}{3}ft^2$

So our answer is:

$\frac{5}{3}ft^2$

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Example Question #1 : How To Find The Area Of A Trapezoid

Rectangles 3

The above diagram shows Rectangle RECT , with midpoint of $\overline{CT}$ .

The area of Quadrilateral REMT is 1,200 . Evaluate .

Possible Answers:

Correct answer:

Explanation:

The easiest way to see this problem is to note that Quadrilateral REMT has as its area that of Rectangle RECT minus that of $\bigtriangleup ECM$ .

The area of Rectangle RECT is its length multiplied by its width:

$2x \cdot \frac{1}{2} x = 2 \cdot \frac{1}{2} \cdot x \cdot x = x^{2}$

is the midpoint of $\overline{CT}$ , so $\bigtriangleup ECM$ has as its base and height $\frac{1}{2} \cdot 2x =x$ and $\frac{1}{2} x$ , respectively;

its area is half their product, or

$\frac{1}{2} \cdot x \cdot \frac{1}{2} x = \frac{1}{4} x^{2}$

The area of Quadrilateral REMT is

$x^{2} - \frac{1}{4} x^{2} = \frac{3}{4} x^{2} = 1,200$ , so

$\frac{3}{4} x^{2} \cdot \frac{4} {3} = 1,200\cdot \frac{4} {3}$

$x^{2} = 1,600$

$x =\sqrt{ 1,600} = 40$

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Example Question #261 : Geometry

The perimeter of the following trapezoid is equal to 23 cm. Solve for . (Figure not drawn to scale.)

Possible Answers:

x=4

x=12

x=2

x=8

Correct answer:

x=4

Explanation:

The perimeter is equal to the sum of all of the sides.

$P=23\: cm$

$P=23\: cm=5+6+x+2x$

23=11+3x

23-11=11+3x-11

12=3x

$\frac{12}{3}=\frac{3x}{3}$

x=4

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Example Question #1 : How To Find The Perimeter Of A Trapezoid

Find the perimeter of the trapezoid:
Question_12

Possible Answers:

$\small 26$

$\small 40$

$\small 23.5$

$\small 21$

Correct answer:

$\small 21$

Explanation:

The perimeter of any shape is equal to the sum of the lengths of its sides:

$\small P=4+6+3+8=21$

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Example Question #261 : Plane Geometry

You recently bought a new bookshelf with a base in the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the arms are 1.5 feet, what is the perimeter of the base of your new bookshelf?

Possible Answers:

Cannot be determined from the information provided.

3.75ft

12ft

8ft

Correct answer:

8ft

Explanation:

To find the perimeter of a bookshelf, we need to add up the lengths of the sides.

We know the two bases, we just need to add the lengths of the arms.

2ft+1.5ft+1.5ft+3ft=8ft

So, our answer is 8ft

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Example Question #1 : Parallelograms

Find the perimeter of the parallelogram.

Possible Answers:

36 in

26 in

18 in

13 in

Correct answer:

26 in

Explanation:

To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.

$P=9+4+9+4=26\: in$

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Example Question #2 : How To Find The Perimeter Of A Parallelogram

If the perimter of a parallelogram is and one of the sides is , what is the other side length?

Possible Answers:

The answer cannot be found

Correct answer:

Explanation:

The perimeter of a parallelogram is found by adding up all four sides.

Since there are two pairs of side with equal lengths, two sides must have a length of .

So the perimeter would be

5+5+l+l=30 or 2l=20 .

To find the value of the other side length, you would divide the remaining perimeter not include in the other sides by .

So $20\div2=10$ .

That means the other side length would be .

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ISEE Middle Level Math : Plane Geometry

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #214 : Geometry

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #2 : How To Find The Area Of A Trapezoid

Example Question #3 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #261 : Geometry

Example Question #1 : How To Find The Perimeter Of A Trapezoid

Example Question #261 : Plane Geometry

Example Question #1 : Parallelograms

Example Question #2 : How To Find The Perimeter Of A Parallelogram

All ISEE Middle Level Math Resources

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