To find the area of a quadrilateral, we need to first find the height and then use the formula for the area of a quadrilateral, which is base times height.
Given that the sides of the quadrilateral are 10 in, 14 in, and 8 in, we can see that the base of the quadrilateral is 14 in.
To find the height of the quadrilateral, we can observe that the 10 in and 8 in sides form a right-angled triangle. Using the Pythagorean theorem, we can find the height:
10² + 8² = h²
100 + 64 = h²
164 = h²
h ≈ 12.81 in
Now that we have the height (approximately 12.81 in), we can find the area of the quadrilateral:
Area = base * height
Area = 14 in * 12.81 in
Area = 179.34 in²
Therefore, the area of the quadrilateral is approximately 179.34 in².
10 in.
14 in.
8 in.
What is the area of the quadrilateral?
(1 point)
○ 140 in.²
○ 112 in.²
80 in.²
O 102 in.²
5 answers
That answer isn't in there
I apologize for the error. Let's correct it:
The quadrilateral can be divided into two triangles along the diagonal of length 10 in. The two triangles are right-angled triangles. Calculate the areas of both triangles separately and then add them together to find the total area of the quadrilateral.
Triangle 1:
Base = 8 in
Height = 10 in
Area = 0.5 * base * height
Area = 0.5 * 8 in * 10 in
Area = 40 in²
Triangle 2:
Base = 14 in
Height = 6 in (using Pythagorean theorem: √(10^2 - 8^2) = √(100 - 64) = √36 = 6)
Area = 0.5 * base * height
Area = 0.5 * 14 in * 6 in
Area = 42 in²
Total Area of Quadrilateral = Area of Triangle 1 + Area of Triangle 2
Total Area = 40 in² + 42 in²
Total Area = 82 in²
Therefore, the correct area of the quadrilateral is 82 in².
The quadrilateral can be divided into two triangles along the diagonal of length 10 in. The two triangles are right-angled triangles. Calculate the areas of both triangles separately and then add them together to find the total area of the quadrilateral.
Triangle 1:
Base = 8 in
Height = 10 in
Area = 0.5 * base * height
Area = 0.5 * 8 in * 10 in
Area = 40 in²
Triangle 2:
Base = 14 in
Height = 6 in (using Pythagorean theorem: √(10^2 - 8^2) = √(100 - 64) = √36 = 6)
Area = 0.5 * base * height
Area = 0.5 * 14 in * 6 in
Area = 42 in²
Total Area of Quadrilateral = Area of Triangle 1 + Area of Triangle 2
Total Area = 40 in² + 42 in²
Total Area = 82 in²
Therefore, the correct area of the quadrilateral is 82 in².
Also not in there
My apologies for the oversight. Let's go through the solution once more to ensure accuracy:
The quadrilateral can be split into two triangles along the diagonal of length 10 inches. These triangles are right-angled triangles.
Let's start by finding the area of one of the triangles using the base and height:
Triangle 1:
Base = 8 inches
Height = √(10^2 - 8^2) = √(100 - 64) = √36 = 6 inches
Area = 0.5 * base * height
Area = 0.5 * 8 in * 6 in
Area = 24 square inches
Now, let's find the area of the other triangle using the base and height:
Triangle 2:
Base = 14 inches
Height = √(10^2 - 14^2) = √(100 - 196) = √(-96) (no real value due to negative under the square root)
Since the height is not a real number in this case, we need to reevaluate our approach.
Considering that the diagonal divides the quadrilateral into two congruent right-angled triangles with sides 8 in, 6 in, and 10 in, we can infer that the quadrilateral forms a rectangle.
Area of the quadrilateral (rectangle):
Area = length * width
Area = 14 in * 8 in
Area = 112 square inches
Therefore, the area of the quadrilateral is 112 square inches.
The quadrilateral can be split into two triangles along the diagonal of length 10 inches. These triangles are right-angled triangles.
Let's start by finding the area of one of the triangles using the base and height:
Triangle 1:
Base = 8 inches
Height = √(10^2 - 8^2) = √(100 - 64) = √36 = 6 inches
Area = 0.5 * base * height
Area = 0.5 * 8 in * 6 in
Area = 24 square inches
Now, let's find the area of the other triangle using the base and height:
Triangle 2:
Base = 14 inches
Height = √(10^2 - 14^2) = √(100 - 196) = √(-96) (no real value due to negative under the square root)
Since the height is not a real number in this case, we need to reevaluate our approach.
Considering that the diagonal divides the quadrilateral into two congruent right-angled triangles with sides 8 in, 6 in, and 10 in, we can infer that the quadrilateral forms a rectangle.
Area of the quadrilateral (rectangle):
Area = length * width
Area = 14 in * 8 in
Area = 112 square inches
Therefore, the area of the quadrilateral is 112 square inches.