Quadrilaterals - Math

Card 0 of 480

Question

The area of square R is 12 times the area of square T. If the area of square R is 48, what is the length of one side of square T?

Answer

We start by dividing the area of square R (48) by 12, to come up with the area of square T, 4. Then take the square root of the area to get the length of one side, giving us 2.

Compare your answer with the correct one above

Question

George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 $ft^{2}$ and costs \$40. One quart of paint covers 100 $ft^{2}$ and costs \$15. How much money will he spend on the blue paint?

Answer

The area of the walls is given by $A = 2wh + 2lh = 2(12)(10) + 2(15)(10) = 540 ft^{2}$

One gallon of paint covers 400 $ft^{2}$ and the remaining 140 $ft^{2}$ would be covered by two quarts.

So one gallon and two quarts of paint would cost

Compare your answer with the correct one above

Question

If the area of rectangle is 52 meters squared and the perimeter of the same rectangle is 34 meters. What is the length of the larger side of the rectangle if the sides are integers?

Answer

Area of a rectangle is = lw

Perimeter = 2(l+w)

We are given 34 = 2(l+w) or 17 = (l+w)

possible combinations of l + w

are 1+16, 2+15, 3+14, 4+13... ect

We are also given the area of the rectangle is 52 meters squared.

Do any of the above combinations when multiplied together= 52 meters squared? yes 4x13 = 52

Therefore the longest side of the rectangle is 13 meters

Compare your answer with the correct one above

Question

Kayla took 25 minutes to walk around a rectangular city block. If the block's width is 1/4 the size of the length, how long would it take to walk along one length?

Answer

Leaving the width to be x, the length is 4_x_. The total perimeter is 4_x_ + 4_x_ + x + x = 10x.

We divide 25 by 10 to get 2.5, the time required to walk the width. Therefore the time required to walk the length is (4)(2.5) = 10.

Compare your answer with the correct one above

Question

A rectangle has a width of 2_x_. If the length is five more than 150% of the width, what is the perimeter of the rectangle?

Answer

Given that w = 2_x_ and l = 1.5_w_ + 5, a substitution will show that l = 1.5(2_x_) + 5 = 3_x_ + 5.

P = 2_w_ + 2_l_ = 2(2_x_) + 2(3_x_ + 5) = 4_x_ + 6_x_ + 10 = 10_x_ + 10 = 10(x + 1)

Compare your answer with the correct one above

Question

Find the perimeter of the following kite:

Answer

The formula for the perimeter of a kite is:

$P = 2(s_{long}) + 2(s_{short})$

Where $s_{long}$ is the length of the longer side and $s_{short}$ is the length of the shorter side

Use the formulas for a triangle and a triangle to find the lengths of the longer sides. The formula for a triangle is $a-a-a \sqrt{2}$ and the formula for a triangle is $a-a \sqrt{3}-2a$ .

Our triangle is: $3 \sqrt{2}m-3 \sqrt{2}m-6m$

Our triangle is: $3 \sqrt{2}m-3 \sqrt{6}m-6\sqrt{2}m$

Plugging in our values, we get:

$P = 2(6\sqrt{2}m) + 2(6m)$

$P = 12\sqrt{2}m + 12m$

Compare your answer with the correct one above

Question

What is the area of a kite with diagonals of 5 and 7?

Answer

To find the area of a kite using diagonals you use the following equation $\frac{ab}{2}=Area: of a: kite$

That diagonals ( and )are the lines created by connecting the two sides opposite of each other.

Plug in the diagonals for and to get $\frac{57}{2}=Area$

Then multiply and divide to get the area. $\frac{35}{2}=17.5$

The answer is

Compare your answer with the correct one above

Question

Find the area of the following kite:

Answer

The formula for the area of a kite is:

$A = \frac{1}{2}(d_{1}\cdot d_{2})$

Where $d_{1}$ is the length of one diagonal and $d_{2}$ is the length of the other diagonal

Plugging in our values, we get:

$A = \frac{1}{2}(d_{1}\cdot d_{2})$

$A = \frac{1}{2}(6m\cdot 13m) = 39m^2$

Compare your answer with the correct one above

Question

Find the area of the following kite:

Answer

The formula for the area of a kite is:

$A = \frac{1}{2} (d_1)(d_2)$

where is the length of one diagonal and is the length of another diagonal.

Use the formulas for a triangle and a triangle to find the lengths of the diagonals. The formula for a triangle is $a-a-a \sqrt{2}$ and the formula for a triangle is $a-a \sqrt{3}-2a$ .

Our triangle is: $3 \sqrt{2}m-3 \sqrt{2}m-6m$

Our triangle is: $3 \sqrt{2}m-3 \sqrt{6}m-6\sqrt{2}m$

Plugging in our values, we get:

$A = \frac{1}{2} (d_1)(d_2)$

$A = \frac{1}{2} (6\sqrt{2}m) (3\sqrt{6}m + 3\sqrt{2}m)$

$A = \frac{1}{2} (18\sqrt{12}+18\sqrt{4}) = 18\sqrt{3}+18m^2$

Compare your answer with the correct one above

Question

Find the perimeter of the following kite:

Answer

In order to find the length of the two shorter edges, use a Pythagorean triple:

In order to find the length of the two longer edges, use the Pythagorean theorem:

$C=3\sqrt{10}m$

The formula of the perimeter of a kite is:

$P = 2(side_{short})+2(side_{long})$

Plugging in our values, we get:

$P = 2(5m)+2(3\sqrt{10}m) = 10+6\sqrt{10}m$

Compare your answer with the correct one above

Question

If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?

Answer

the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.

The area of the rectangle can be determined from multiplying length by width, so,

4 x 8 = 32 inches squared

Compare your answer with the correct one above

Question

Find the measure of angle in the isosceles trapezoid pictured below.

Answer

The sum of the angles in any quadrilateral is 360°, and the properties of an isosceles trapezoid dictate that the sets of angles adjoined by parallel lines (in this case, the bottom set and top set of angles) are equal. Subtracting 2(72°) from 360° gives the sum of the two top angles, and dividing the resulting 216° by 2 yields the measurement of x, which is 108°.

Compare your answer with the correct one above

Question

What is the area of this regular trapezoid?

Answer

To solve this question, you must divide the trapezoid into a rectangle and two right triangles. Using the Pythagorean Theorem, you would calculate the height of the triangle which is 4. The dimensions of the rectangle are 5 and 4, hence the area will be 20. The base of the triangle is 3 and the height of the triangle is 4. The area of one triangle is 6. Hence the total area will be 20+6+6=32. If you forget to split the shape into a rectangle and TWO triangles, or if you add the dimensions of the trapezoid, you could arrive at 26 as your answer.

Compare your answer with the correct one above

Question

What is the area of the trapezoid above if a = 2, b = 6, and h = 4?

Answer

Area of a Trapezoid = ½(a+b)h

= ½ (2+6) 4

= ½ (8) * 4

= 4 * 4 = 16

Compare your answer with the correct one above

Question

A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?

Answer

In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:

area of trapezoid = (1/2)(4 + s)(s)

Similarly, the area of a square with sides of length a is given by _a_2. Thus, the area of the square given in the problem is _s_2.

We now can set the area of the trapezoid equal to the area of the square and solve for s.

(1/2)(4 + s)(s) = _s_2

Multiply both sides by 2 to eliminate the 1/2.

(4 + s)(s) = 2_s_2

Distribute the s on the left.

4_s_ + _s_2 = 2_s_2

Subtract _s_2 from both sides.

4_s_ = _s_2

Because s must be a positive number, we can divide both sides by s.

4 = s

This means the value of s must be 4.

The answer is 4.

Compare your answer with the correct one above

Question

This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in.

What is the area of the isoceles trapezoid?

Answer

In order to find the area of an isoceles trapezoid, you must average the bases and multiply by the height.

The average of the bases is straight forward:

$\frac{6+18}{2}=12$

In order to find the height, you must draw an altitude. This creates a right triangle in which one of the legs is also the height of the trapezoid. You may recognize the Pythagorean triple (6-8-10) and easily identify the height as 8. Otherwise, use $a^{2}+b^{2}=c^{2}$ .

$36+b^{2}=100$

$b^{2}=64$

Multiply the average of the bases (12) by the height (8) to get an area of 96.

Compare your answer with the correct one above

Question

The front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?

Answer

Glass Area per Window = 8 ft x 6 ft = 48 ft2

Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows

Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft2

Compare your answer with the correct one above

Question

Find the area of the following trapezoid:

Answer

The formula for the area of a trapezoid is:

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

Where is the length of one base, is the length of the other base, and is the height.

To find the height of the trapezoid, use a Pythagorean triple:

Plugging in our values, we get:

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

$A = \frac{1}{2}(16m+26m)(12m)=252m^2$

Compare your answer with the correct one above

Question

Find the area of the following trapezoid:

Answer

Use the formula for triangles in order to find the length of the bottom base and the height.

The formula is:

$a-a\sqrt{3}-2a$

Where is the length of the side opposite the $\measuredangle 30$ .

Beginning with the side, if we were to create a triangle, the length of the base is $6\sqrt{3}m$ , and the height is .

Creating another triangle on the left, we find the height is , the length of the base is $2\sqrt{3}m$ , and the side is $4\sqrt{3}m$ .

The formula for the area of a trapezoid is:

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

Where is the length of one base, is the length of the other base, and is the height.

Plugging in our values, we get:

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

$A = \frac{1}{2}(16m+16m+6\sqrt{3}m+2\sqrt{3}m)(6m)$

$A = \frac{1}{2}(32m+8\sqrt{3}m)(6m)$

$A = (32m+8\sqrt{3}m)(3m)=96+24\sqrt{3}m^2$

Compare your answer with the correct one above

Question

Determine the area of the following trapezoid:

Answer

The formula for the area of a trapezoid is:

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

where is the length of one base, is the length of another base, and is the length of the height.

Plugging in our values, we get:

$A=\frac{1}{2}(7m+5m)(4m)=24m^2$

Compare your answer with the correct one above

Tap the card to reveal the answer