To find the area of the shaded sections of the trapezoid, we first need to calculate the total area of the trapezoid.
The formula to calculate the area of a trapezoid is:
Area = (1/2) * (a + b) * h
Where:
a = length of one base (9 inches)
b = length of the other base (7 inches)
h = height of the trapezoid (5.2 inches)
Plugging in the values:
Total area = (1/2) * (9 + 7) * 5.2
Total area = (1/2) * 16 * 5.2
Total area = 8 * 5.2
Total area = 41.6 square inches
Now, we need to find the area of the two shaded sections. One of the shaded sections is a triangle and the other is a smaller trapezoid formed by the two bases and the transversal line.
The area of the triangle can be calculated using the formula:
Area = (1/2) * base * height
The base of the triangle is 1.7 inches and the height is 5.2 inches. So, the area of the shaded triangle = 1/2 * 1.7 * 5.2 = 4.42 square inches.
The area of the smaller trapezoid can be calculated the same way as the total area of the trapezoid, but with different base lengths. The bases are 4.7 inches and 5.2 inches, and the height is still 5.2 inches. Thus, the area of the shaded trapezoid = 1/2 * (4.7 + 5.2) * 5.2 = 1/2 * 9.9 * 5.2 = 25.74 square inches.
Therefore, to find the total area of the shaded sections of the trapezoid, you add the areas of the triangle and trapezoid:
Total area of shaded sections = 4.42 + 25.74 = 30.16 square inches.
What is the total area, in square inches, of the shaded sections of the trapezoid below?9,7,5.2,4.7
5 answers
that isnt right
My apologies for the error. Let's reevaluate the calculation.
Since the bases of the trapezoid are 9 inches and 7 inches, and the height is 5.2 inches, the total area of the trapezoid is:
Total Area = (1/2) * (9 + 7) * 5.2
Total Area = 8 * 5.2
Total Area = 41.6 square inches
Next, we need to calculate the areas of the shaded sections. One is a triangle and the other is a smaller trapezoid.
Area of the triangle = (1/2) * base * height
Area of the triangle = (1/2) * 1.7 * 5.2 = 4.42 square inches
To find the area of the shaded trapezoid, we first need to find the base length of the shaded trapezoid by subtracting the base lengths of the trapezoid from the total base length:
Base length of the shaded trapezoid = 9 - 7 = 2 inches
Now, we can calculate the area of the shaded trapezoid using the base length, height, and the formula for the area of a trapezoid:
Area of the shaded trapezoid = (1/2) * (2 + 5.2) * 5.2
Area of the shaded trapezoid = (1/2) * 7.2 * 5.2
Area of the shaded trapezoid = 18.72 square inches
To find the total area of the shaded sections, we add the areas of the triangle and the shaded trapezoid:
Total area of shaded sections = 4.42 + 18.72 = 23.14 square inches
Therefore, the total area of the shaded sections in the trapezoid is 23.14 square inches.
Since the bases of the trapezoid are 9 inches and 7 inches, and the height is 5.2 inches, the total area of the trapezoid is:
Total Area = (1/2) * (9 + 7) * 5.2
Total Area = 8 * 5.2
Total Area = 41.6 square inches
Next, we need to calculate the areas of the shaded sections. One is a triangle and the other is a smaller trapezoid.
Area of the triangle = (1/2) * base * height
Area of the triangle = (1/2) * 1.7 * 5.2 = 4.42 square inches
To find the area of the shaded trapezoid, we first need to find the base length of the shaded trapezoid by subtracting the base lengths of the trapezoid from the total base length:
Base length of the shaded trapezoid = 9 - 7 = 2 inches
Now, we can calculate the area of the shaded trapezoid using the base length, height, and the formula for the area of a trapezoid:
Area of the shaded trapezoid = (1/2) * (2 + 5.2) * 5.2
Area of the shaded trapezoid = (1/2) * 7.2 * 5.2
Area of the shaded trapezoid = 18.72 square inches
To find the total area of the shaded sections, we add the areas of the triangle and the shaded trapezoid:
Total area of shaded sections = 4.42 + 18.72 = 23.14 square inches
Therefore, the total area of the shaded sections in the trapezoid is 23.14 square inches.
that isn right
Apologies for the oversight. Let's reevaluate the calculation of the total area of the shaded sections in the trapezoid.
The total area of the trapezoid is calculated as follows:
Total Area of Trapezoid = (1/2) * (a + b) * h
Total Area of Trapezoid = (1/2) * (9 + 7) * 5.2
Total Area of Trapezoid = (1/2) * 16 * 5.2
Total Area of Trapezoid = 8 * 5.2
Total Area of Trapezoid = 41.6 square inches
Next, let's calculate the area of the shaded sections:
1. Triangle:
Area of Triangle = (1/2) * base * height
Area of Triangle = (1/2) * 1.7 * 5.2
Area of Triangle = 8.36 square inches
2. Trapezoid
To find the area of the shaded trapezoid, we first calculate the base length of the shaded trapezoid by subtracting the base lengths of the trapezoid:
Base length of shaded trapezoid = 9 - 7 = 2 inches
Next, we calculate the area of the shaded trapezoid:
Area of Shaded Trapezoid = (1/2) * (2 + 5.2) * 5.2
Area of Shaded Trapezoid = (1/2) * 7.2 * 5.2
Area of Shaded Trapezoid = 18.72 square inches
Now, to find the total area of the shaded sections, we add the areas of the triangle and the shaded trapezoid:
Total Area of Shaded Sections = 8.36 + 18.72 = 27.08 square inches
Therefore, the correct total area of the shaded sections in the trapezoid is 27.08 square inches. Thank you for your patience.
The total area of the trapezoid is calculated as follows:
Total Area of Trapezoid = (1/2) * (a + b) * h
Total Area of Trapezoid = (1/2) * (9 + 7) * 5.2
Total Area of Trapezoid = (1/2) * 16 * 5.2
Total Area of Trapezoid = 8 * 5.2
Total Area of Trapezoid = 41.6 square inches
Next, let's calculate the area of the shaded sections:
1. Triangle:
Area of Triangle = (1/2) * base * height
Area of Triangle = (1/2) * 1.7 * 5.2
Area of Triangle = 8.36 square inches
2. Trapezoid
To find the area of the shaded trapezoid, we first calculate the base length of the shaded trapezoid by subtracting the base lengths of the trapezoid:
Base length of shaded trapezoid = 9 - 7 = 2 inches
Next, we calculate the area of the shaded trapezoid:
Area of Shaded Trapezoid = (1/2) * (2 + 5.2) * 5.2
Area of Shaded Trapezoid = (1/2) * 7.2 * 5.2
Area of Shaded Trapezoid = 18.72 square inches
Now, to find the total area of the shaded sections, we add the areas of the triangle and the shaded trapezoid:
Total Area of Shaded Sections = 8.36 + 18.72 = 27.08 square inches
Therefore, the correct total area of the shaded sections in the trapezoid is 27.08 square inches. Thank you for your patience.
1 answer