What is the area of the quadrilateral
12 in. Left side Length, 10in. Right side length, 8 in. Top width
In one triangle
To find the area of one triangle in the quadrilateral, you can use the formula for the area of a triangle:
Area = (base * height) / 2
Choose one of the triangles formed by the diagonal and use the following measurements:
- Base (bottom edge of the triangle) = 8 inches
- Height = 8√5 inches (calculated in the previous response)
Substitute these values into the formula:
Area = (8 * 8√5) / 2 = 32√5 square inches
Therefore, the area of one triangle in the quadrilateral is 32√5 square inches.
No triangles
To find the area of the quadrilateral without splitting it into triangles, you can use the formula for the area of a trapezoid, which is given by the formula:
Area = (1/2) * (sum of the lengths of the parallel sides) * (height)
In this case, the left and right sides are the parallel sides of the quadrilateral, and the height is the length of the top side (width of the quadrilateral).
Given:
Left side length = 12 inches
Right side length = 10 inches
Top width = 8 inches
Substitute these values into the formula:
Area = (1/2) * (12 + 10) * 8
Area = (1/2) * 22 * 8
Area = 11 * 8
Area = 88 square inches
Therefore, the area of the quadrilateral is 88 square inches.
To find the area of a quadrilateral, you can split it into two triangles and find the area of each triangle separately.
First, find the height of the quadrilateral. Since the left and right sides are not perpendicular to the top, you can create a right triangle with the height as one of the legs, the left side as the hypotenuse, and the top as the other leg. Using the Pythagorean theorem, the height is √(12^2 - 8^2) = √(144 - 64) = √80 = 8√5 in.
Now you can find the area of each triangle:
1st triangle: (1/2) * 8 * 8√5 = 32√5 in^2
2nd triangle: (1/2) * 10 * 8√5 = 40√5 in^2
Adding the areas of the two triangles together gives a total area of 32√5 + 40√5 = 72√5 square inches.