Cara and Beejal make a poster for school. The poster is in the shape of a rectangle. The left side of the poster measures 7 units; the top side of the poster measures 6 units. What is the area in square units of the completed poster?
13 square units
48 square units
26 square units
42 square units
The area of a rectangle is found by multiplying the length by the width. In this case, the length is 7 units and the width is 6 units. So, the area is:
7 x 6 = 42 square units
Therefore, the correct answer is 42 square units.
The formula for the area of a triangle is:
area = (1/2) x base x height
where base and height are the length of the base and the height of the triangle, respectively.
In this case, we know that the area is 7.5 square feet, the height is 2.5 feet, so we can solve for the base:
7.5 = (1/2) x base x 2.5
Multiplying both sides by 2 and dividing by 2.5, we get:
base = 6 feet
Therefore, the length of the base of Ja'Miles' sign is 6 feet. Answer: \boxed{6 \text{ feet}}
In that case, the closest answer would be 31 square miles as it is the only option greater than 28 (which is the sum of the areas of the two rectangles) but less than 40 (which is the actual total area of the composite figure). However, it is still not the correct answer as none of the given options is exact.
The area of the rectangle is:
9 cm x 3 cm = 27 square cm
The area of each triangle is:
(1/2) x 2 cm x 3 cm = 3 square cm
Therefore, the total area of the piece of jewelry is:
27 square cm + 3 square cm + 3 square cm = 33 square cm
So, the answer is \boxed{33 \text{ square centimeters}}.
Ja’Miles designs a sign for a store in the shape of a triangle. His design is 7.5 square feet in area, and the triangle has a height of 2.5 feet. What is the length of the base of his sign?
3 feet
0.6 feet
6 feet
10 feet
An illustration shows a rectangle extending upward on the top left and top right sides forming two more rectangles of varying width and length. The dimensions are as follows: The bottom of the rectangle is 7 miles. The extended left side is 6 miles. The vertical height of the left side rectangular extension is 3 miles. The vertical and horizontal lengths of the right side rectangular extension is 1 mile each. There are six right angle symbols at the vertices of the polygon.
What is the area of the composite figure?
31 square miles
25 square miles
28 square miles
21 square miles
Use the image to answer the question.
A composite shape is drawn using a rectangle and 2 triangles. A horizontally aligned rectangle is 9 centimeters long and 3 centimeters wide. A right triangle facing upward adjoins the rectangle on the left side marked 3 centimeters. A right triangle facing downward adjoins the rectangle on the right side. The base leg of both triangles measures 2 centimeters.
Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?
39 square centimeters
33 square centimeters
27 square centimeters
30 square centimeters
ethan writes the ratio x8=y16 to help him reduce the size of a two-dimensional shape. If the new value of y is 3 units, what will be the value of x?(1 point)
Responses
1.5 units
316 units
0.5 units
6 units
We can solve for x by cross-multiplying the given ratio:
x8 = y16
Multiplying both sides by 16, we get:
16x = 8y
Substituting y = 3, we get:
16x = 8(3)
16x = 24
Dividing both sides by 16, we get:
x = 24/16 = 3/2 = 1.5
So, the value of x is \boxed{1.5 \text{ units}}.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is pi, and r is the radius.
Substituting the given value, we get:
C = 2 x 3.14 x 90
C = 565.2
Rounding to the tenths place, we get:
C ≈ \boxed{565.2}
The formula for the circumference of a circle is:
C = πd
where C is the circumference, π is pi, and d is the diameter.
Substituting the given value, we get:
C = 3.14 x 379
C = 1190.06
Rounding to the hundredths place, we get:
C ≈ \boxed{1190.06}
The radius of a circle is 98 mm. What is the area of the circle? Write your answer to the hundredths place. Use 3.14 for π.(1 point)
just pick one out of the four
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph?
2 inches by 1 inch
12 inches by 8 inches
1 inch by 0.5 inches
1.5 inches by 1 inch
To create a smaller scale drawing of the photograph, we need to use dimensions that are proportionally smaller. That means we need to multiply the original dimensions by the same scale factor to get the new dimensions. Since we want a smaller scale, we need to use a scale factor less than 1.
Let's use the scale factor "s" to represent the reduction in size. We want the new dimensions to be 6s inches by 4s inches.
Out of the given answer choices, the dimensions that satisfy this requirement are 1.5 inches by 1 inch, if we take the scale factor s = 1/4.
6s = 6(1/4) = 1.5
4s = 4(1/4) = 1
Therefore, a smaller scale drawing of the original photograph would have dimensions of \boxed{1.5 \text{ inches by 1 inch}}.
Use the image to answer the question.
An illustration shows a triangle with a base labeled 8 inches. A line runs through the center of the triangle from the apex to the base. This perpendicular height is labeled 5 inches.
Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?
3.2 square inches
1.6 square inches
20 square inches
6.4 square inches
What is the approximate circumference of a circle that has a radius of 90? Use 3.14 for π and express your answer to the tenths place.(1 point)
What is the approximate circumference of a circle that has a diameter of 379? Use 3.14 for π and express your answer to the hundredths place. (1 point)
The approximate circumference of a circle is 7,459 miles. What is the diameter rounded to the nearest hundredths place? Use 3.14 for π.(1 point)
If the area of a circle is 28.26 cm2, what is the radius of the circle?
The formula for the area of a circle is:
A = πr^2
where A is the area of the circle, π is pi, and r is the radius of the circle. To solve for the radius, we can rearrange the formula as:
r = sqrt(A/π)
Substituting the given value for A, we get:
r = sqrt(28.26 cm^2 / 3.14)
r ≈ \boxed{3} cm
So, the radius of the circle is approximately 3 cm.
Complete the table by finding the circumference and area of a circle with a radius of 279 inches. Substitute 3.14 for pi. Express your answers to the hundredths place.
Radius Circumference Area
279 in. in. in.2
A triangular flag has a height of 15 inches and a base length of 25 inches. Magnolia makes a scale drawing of the flag in which the base length is 10 inches. What is the area of Magnolia’s scale drawing? Solve the problem by computing the actual area from the scale drawing. Show your work.
We can use ratios to find the height of the scale drawing:
25 inches (actual base length) : 15 inches (actual height) :: 10 inches (scaled base length) : x (scaled height)
Using cross-multiplication:
25 in. x = 15 in. x 10 in.
x = 150 in² / 25 in.
x = 6 in. (scaled height)
Therefore, the scale factor is:
15 in. (actual height) / 6 in. (scaled height) = 2.5
The area of the actual triangle is given by the formula:
A = (1/2)bh
where b is the base length and h is the height. Substituting the given values, we get:
A = (1/2)(25 in.)(15 in.)
A = 187.5 in²
The area of the scale drawing is equal to the actual area divided by the square of the scale factor:
A(scale) = A(actual) / scale factor²
A(scale) = 187.5 in² / 2.5²
A(scale) = 187.5 in² / 6.25
A(scale) = 30 in²
Therefore, the area of Magnolia's scale drawing is \boxed{30 \text{ in²}}.
I don't get it
To find the area of Magnolia's scale drawing, we need to first find the height of the scaled triangle. We can do this using ratios.
We know that the actual height of the triangle is 15 inches and the actual base length is 25 inches. We also know that the scaled base length is 10 inches. We can set up a ratio:
25 inches (actual base length) : 15 inches (actual height) :: 10 inches (scaled base length) : x (scaled height)
To solve for x, we can cross-multiply:
25 in. x = 15 in. x 10 in.
Simplifying, we get:
x = 150 in² / 25 in.
x = 6 in.
So, the height of the scaled triangle is 6 inches.
The scale factor is the ratio of the actual height to the scaled height:
15 in. (actual height) / 6 in. (scaled height) = 2.5
Now, we need to find the area of the scaled triangle using the actual area and the square of the scale factor.
The actual area of the triangle is given by the formula:
A = (1/2)bh
where b is the base of the triangle and h is the height. Substituting the given values, we get:
A = (1/2)(25 in.)(15 in.)
A = 187.5 in²
The scale factor is 2.5, so we can find the area of the scaled triangle by dividing the actual area by the square of the scale factor:
A(scale) = A(actual) / scale factor²
A(scale) = 187.5 in² / 2.5²
A(scale) = 187.5 in² / 6.25
A(scale) = 30 in²
Therefore, the area of Magnolia's scale drawing is 30 square inches.
The composite figure consists of two rectangles, one with dimensions 7 miles by 3 miles (on the left side) and one with dimensions 1 mile by 7 + 6 = 13 miles (on the right side), and a parallelogram on top with base 6 miles and height 2 miles (the sum of the heights of the two rectangles).
The area of the first rectangle is 7 miles × 3 miles = 21 square miles.
The area of the second rectangle is 1 mile × 13 miles = 13 square miles.
The area of the parallelogram is (1/2) × 6 miles × 2 miles = 6 square miles.
Therefore, the total area of the composite figure is:
21 square miles + 13 square miles + 6 square miles = 40 square miles
So, none of the given options is correct.
The area of a triangle is found by multiplying the base by the height and dividing by 2. In this case, the height is 5 inches and the base is 8 inches, so the area of the original triangle is:
(8 in. x 5 in.) / 2 = 40 in² / 2 = 20 in²
The scale factor for the height is:
5 in. / 2 in. = 2.5
So, the height of the scaled triangle is 2 in. x 2.5 = 5 in.
The base of the scaled triangle is also reduced by a factor of 2.5:
8 in. / 2.5 = 3.2 in.
The area of the scaled triangle is found using the same formula as before, but with the base and height in scaled units:
(3.2 in. x 5 in.) / 2 = 16 in² / 2 = 8 in²
Therefore, the area of Crystal's scale drawing is \boxed{8 \text{ square inches}}.
The formula for the area of a circle is:
A = πr^2
where A is the area, π is pi, and r is the radius.
Substituting the given value, we get:
A = 3.14 x (98 mm)^2
A = 30171.64 mm^2
Rounding to the hundredths place, we get:
A ≈ \boxed{30171.64}
To find the circumference of a circle with radius 279 inches, we can use the formula:
C = 2πr
Substituting the given value of the radius and approximating π to be 3.14, we get:
C = 2 x 3.14 x 279
C ≈ 1751.32 inches
Rounding this to the hundredths place, the circumference is approximately 1751.32 inches.
To find the area of the circle with radius 279 inches, we can use the formula:
A = πr^2
Substituting the given value of the radius and approximating π to be 3.14, we get:
A = 3.14 x 279^2
A ≈ 245161.86 square inches
Rounding this to the hundredths place, the area is approximately 245161.86 square inches.
So, the completed table is:
Radius Circumference Area
279 in. 1751.32 in. 245161.86 in.2
The formula for the circumference of a circle is:
C = πd
where C is the circumference, π is pi, and d is the diameter.
Substituting the given value, we get:
7459 = 3.14 x d
Dividing both sides by 3.14, we get:
d ≈ 2371.34
Rounding to the nearest hundredths place, we get:
d ≈ \boxed{2371.33}