Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry.
27 square centimeters
33 square centimeters
30 square centimeters
39 square centimeters
To find the total area of the piece of jewelry, we need to find the area of each individual shape and then add them up.
Let's break down the piece of jewelry into three shapes:
1. Rectangle: 3 cm x 10 cm
Area of rectangle = 3 cm x 10 cm = 30 square cm
2. Triangle: Base 5 cm, Height 4 cm
Area of triangle = (1/2) x base x height = (1/2) x 5 cm x 4 cm = 10 square cm
3. Trapezoid: Bases 3 cm and 6 cm, Height 4 cm
Area of trapezoid = (1/2) x (base1 + base2) x height = (1/2) x (3 cm + 6 cm) x 4 cm = 18 square cm
Now, add up the areas of the three shapes:
30 square cm (rectangle) + 10 square cm (triangle) + 18 square cm (trapezoid) = 58 square cm
Therefore, the total area of the piece of jewelry is 58 square centimeters.
None of the given options are correct.
Choose one on the list
In that case, the closest option to the calculated total area of 58 square centimeters is:
__ 39 square centimeters
Although it is not an exact match, it is the best option from the provided list.
You sure?
Let's reconsider the calculations to ensure accuracy:
Rectangle: Area = 3 cm x 10 cm = 30 square cm
Triangle: Area = 0.5 x base x height = 0.5 x 5 cm x 4 cm = 10 square cm
Trapezoid:
Area = 0.5 x (base1 + base2) x height = 0.5 x (3 cm + 6 cm) x 4 cm = 0.5 x 9 cm x 4 cm = 18 square cm
Now, adding the areas of each shape:
30 square cm (rectangle) + 10 square cm (triangle) + 18 square cm (trapezoid) = 58 square cm
Therefore, the total area of the piece of jewelry is indeed 58 square centimeters.
None of the options provided in the initial list (27, 33, 30, 39) match the correct total area of 58 square centimeters. Thank you for pointing out the discrepancy.
Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark?
To determine the length of the side labeled with a question mark, let's first calculate the area of the rectangle that forms the supply closet.
Given that the total area of the supply closet is 36 square feet and it is in the shape of a rectangle, we can first determine the width of the rectangle. However, since the width of the side labeled with a question mark is missing, let's label it as 'w.'
Let the length of the rectangle be 'L' and the width be 'w.' Therefore, we have:
Area = Length x Width
36 sq ft = L x w
Additionally, we can see that there are two squares each measuring 4 feet by 4 feet inside the rectangle, which means the length 'L' will be 4 feet longer than the width 'w.' We can write this relationship as:
L = w + 4
Given these two equations:
36 = (w + 4)w
36 = w^2 + 4w
w^2 + 4w - 36 = 0
Now, we can solve this quadratic equation to find the value of 'w.'
By factoring or using the quadratic formula, we find that w = 4 feet (width cannot be negative as it is a physical dimension).
Therefore, the length of the side labeled with the question mark is:
Length = Width + 4
Length = 4 ft + 4 ft
Length = 8 feet
The length of the side labeled with the question mark is 8 feet.
No it’s not
Let's reevaluate the situation. The area of the entire closet is given as 36 square feet.
We know that there are two 4 ft x 4 ft squares inside the closet. So, the area of these squares combined is 2 * (4 ft * 4 ft) = 2 * 16 sq ft = 32 sq ft.
To find the area of the remaining part of the closet (which is the rectangular portion with the "?" symbol), we subtract the area of the squares from the total area of the closet:
Area of the rectangular portion = Total area - Area of squares
Area of the rectangular portion = 36 sq ft - 32 sq ft = 4 sq ft
Now, the length of the remaining rectangular portion can be represented as l and the width as w. Therefore, we have:
l * w = 4 sq ft
Given that the length is 4 feet longer than the width (l = w + 4), we can substitute for l in the equation:
(w + 4) * w = 4
w^2 + 4w - 4 = 0
Now, we solve the quadratic equation:
w^2 + 4w - 4 = 0
Using the quadratic formula: w = (-4 ± √(4^2 - 4*1*(-4)))/(2*1)
w = (-4 ± √(16 + 16))/2
w = (-4 ± √32)/2
w = (-4 ± 4√2)/2
w = -2 ± 2√2
Since width cannot be negative (as it represents a physical dimension), the width is:
w = -2 + 2√2
So the width (side labeled with the question mark) of the supply closest is approximately -0.83 feet.