Question 1

For a rectangle with base length of 1 foot and height 6 inches, the area is 6  .

Accepted Answer

To find the area of a rectangle, we multiply the base length by the height.

Base length = 1 foot = 12 inches 
Height = 6 inches

Area = base length x height 
Area = 12 inches x 6 inches 
Area = 72 square inches

Therefore, the area of the rectangle is 72 square inches, not 6 11ebfb55_24bb_2b2d_9d86_0197146e9a37_TBX8811_11.

Question 2

Find the exact area of a triangle whose sides measure 5, 6, and 7.
A)  
B)  
C)  
D)None of These

Accepted Answer

The answer of Find the exact area of a triangle...

Question 3

For an isosceles triangle with length of leg s and length of base b, the perimeter Pis given by P = 2s + b.

Accepted Answer

This is the correct formula for the perimeter of an isosceles triangle, with two equal sides of length s and a base of length b.

Question 4

For regular pentagon ABCDE , diagonals  and  are drawn to form  . Find m  .

Accepted Answer

The answer of For regular pentagon ABCDE , diagonals ...

Question 5

. If AB = 4, XY = 10, and the area of  is 7.8  , find the area of

Accepted Answer

The answer of        . If...

Question 6

For any quadrilateral with perpendicular diagonals of lengths  and  , the area is 
given by A =    .

Accepted Answer

The answer of For any quadrilateral with perpendicular diagonals of...

Question 7

In  ,        . If MQ = 10, RP = 4, and MR = 8, find the area of  .

Accepted Answer

The answer of In  ,      ...

Question 8

The diagonals of quadrilateral ABCD are perpendicular. If AC = 14 inches and BD = 25 inches, find the area of ABCD.

Accepted Answer

The answer of The diagonals of quadrilateral ABCD are perpendicular....

Question 9

The semiperimeter s of a triangle with sides of lengths a , b , and c is given by s =  ( a + b + c ).

Accepted Answer

The answer of The semiperimeter s of a triangle with...

Question 10

In isosceles trapezoid HJKL ,        . If m  = 45 ° , JK = 6 cm, and the length of an altitude is 4 cm, find the exact perimeter of HJKL .
A)(20 + 4  )cm
B)(20 + 8  )cm
C)(20 + 4  )cm
D)(20 + 8  )cm

Accepted Answer

We can begin by drawing a diagram of the trapezoid and labeling the given information:

[asy]
pair h,j,k,l,X,Y;
h = (0,0);
j = (1,4);
k = (5,4);
l = (6,0);
X = (1,0);
Y = (5,0);
draw(h--j--k--l--h);
draw(j--X,dashed);
draw(k--Y,dashed);
label("$H$",h,SW);
label("$J$",j,N);
label("$K$",k,N);
label("$L$",l,SE);
label("$X$",X,S);
label("$Y$",Y,S);
label("$6$",j--k,N);
label("$4$",X--j,W);
draw(rightanglemark(j,X,h,8));
[/asy]

We can use the fact that opposite angles in an isosceles trapezoid are congruent to find that $\angle J = \angle K = 67.5^\circ$. Moreover, we have $\angle JXH + \angle KLY = 180^\circ$ since they are supplementary. Thus, we can find that $\angle KLY = 112.5^\circ$.

Since $	riangle JXY$ is a right triangle, we can use trigonometry to find that $JX = 4\cot(45^\circ) = 4$. Similarly, we can find that $KY = 4\cot(112.5^\circ) \approx 1.38$.

Using the Pythagorean Theorem, we can find that $JL = \sqrt{(JK + KY)^2 + 4^2}$. Plugging in our values, we get 
$$JL = \sqrt{(6+1.38)^2 + 4^2} = \sqrt{45.3} \approx 6.72.$$

Finally, the perimeter of the trapezoid is $HL + JK + KL + JL$. Plugging in our values, we get 
$$HL = KL = 2\cdot JX = 2\cdot 4= 8,$$
so the perimeter is 
$$HL + JK + KL + JL = 8+6+8+\sqrt{45.3}= 22+\sqrt{45.3} = 20 + 8\sqrt{2}.$$
Thus, the answer is $\boxed{	extbf{(B)}}$.

Question 11

A triangle has a perimeter of 40 and area of 60. Using A =  rP , find the length 
of radius r for the inscribed circle for this triangle.

Accepted Answer

The answer of A triangle has a perimeter of 40...

Question 12

Find the area of the triangle whose sides have lengths 13 cm, 14 cm, and 15 cm.

Accepted Answer

The answer of Find the area of the triangle whose...

Question 13

If both a parallelogram and triangle have the same base and altitude, then thearea of the parallelogram is twice the area of the triangle.

Accepted Answer

Let's assume that the base and altitude of both the parallelogram and triangle are b and h respectively.

The area of the parallelogram = base x altitude = b x h

The area of the triangle = base x altitude / 2 = b x h / 2

Therefore, the area of the parallelogram is:

b x h

And the area of the triangle is:

b x h / 2

Dividing the area of the parallelogram by the area of the triangle, we get:

(b x h) / (b x h / 2) = 2

Hence, the area of the parallelogram is twice the area of the triangle. Therefore, the option A is correct.

Question 14

In  ,        and        . How are  and  related?
A)congruent
B)same perimeters
C)same areas
D)similar

Accepted Answer

The given hexadecimal strings are not specific enough to determine the shape, size, or location of the figures being represented. Therefore, it is impossible to determine if the figures are congruent or have the same perimeter or area. The only relation that can be inferred is that they are likely similar, as they share the same code prefix and suffix.

Question 15

Find the length of base in an isosceles triangle with perimeter 25 inches and length of leg8 inches.

Accepted Answer

The answer of Find the length of base in an...

Question 16

For the triangle with sides of lengths a, b, and c, find an expression for the semiperimeter s of the triangle.

Accepted Answer

The answer of For the triangle with sides of lengths...

Question 17

If    , then the altitude to base  of  is  .

Accepted Answer

The given information does not provide any connection between the altitude to base 11ebfb55_24bb_041a_9d86_1f7ad4636783_TBX8811_11 and the other coordinates mentioned. Therefore, it is not possible to determine the altitude.

Question 18

The area of  is 35.1  . Choosing a side of RSTV that measures 4.5 cm as the base, what is the length of the corresponding altitude?
A)7.8 cm
B)8.2 cm
C)15.6 cm
D)None of These

Accepted Answer

The answer of The area of  is 35.1 ...

Question 19

Find the perimeter of rhombus RSTV in which the lengths of diagonals are RT = 24 in and SV = 10 in.

Accepted Answer

The answer of Find the perimeter of rhombus RSTV in...

Question 20

For rectangle ABCD, AB = 5 inches while the length of a diagonal is AC = 13 inches. Find the area of the rectangle.

Accepted Answer

The answer of For rectangle ABCD, AB = 5 inches...

Quiz 9: Areas of Polygons and Circles

For a rectangle with base length of 1 foot and height 6 inches, the area is 6 .

Find the exact area of a triangle whose sides measure 5, 6, and 7.

For an isosceles triangle with length of leg s and length of base b, the perimeter Pis given by P = 2s + b.

For regular pentagon ABCDE , diagonals and are drawn to form . Find m .

. If AB = 4, XY = 10, and the area of is 7.8 , find the area of

For any quadrilateral with perpendicular diagonals of lengths and , the area is given by A = .

In , . If MQ = 10, RP = 4, and MR = 8, find the area of .

The diagonals of quadrilateral ABCD are perpendicular. If AC = 14 inches and BD = 25 inches, find the area of ABCD.

The semiperimeter s of a triangle with sides of lengths a , b , and c is given by s = ( a + b + c ).

In isosceles trapezoid HJKL , . If m = 45 ° , JK = 6 cm, and the length of an altitude is 4 cm, find the exact perimeter of HJKL .

A triangle has a perimeter of 40 and area of 60. Using A = rP , find the length of radius r for the inscribed circle for this triangle.

Find the area of the triangle whose sides have lengths 13 cm, 14 cm, and 15 cm.

If both a parallelogram and triangle have the same base and altitude, then thearea of the parallelogram is twice the area of the triangle.

In , and . How are and related?

Find the length of base in an isosceles triangle with perimeter 25 inches and length of leg8 inches.

For the triangle with sides of lengths a, b, and c, find an expression for the semiperimeter s of the triangle.

If , then the altitude to base of is .

The area of is 35.1 . Choosing a side of RSTV that measures 4.5 cm as the base, what is the length of the corresponding altitude?

Find the perimeter of rhombus RSTV in which the lengths of diagonals are RT = 24 in and SV = 10 in.

For rectangle ABCD, AB = 5 inches while the length of a diagonal is AC = 13 inches. Find the area of the rectangle.