CAN SOMEONE EXPLAIN HOW THE ANSWER IS 38 AND WHAT STEPS IM NOT GETTING IT
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The vertical left edge of a trapezoid is 8 inches and meets the bottom edge of the trapezoid at a right angle. The bottom edge is 4 inches and meets the vertical right edge at a right angle. The right edge is 11 inches. The top slanted edge measures 5 in
Calculate the area of the trapezoid, which is not drawn to scale...
To find the area of the trapezoid, we will need to know the length of the top edge (which is parallel to the bottom edge) and the height of the trapezoid. Since we have the length of the slant height (5 inches) and the difference in height between the left and right edges (11 - 8 = 3 inches), we can use the Pythagorean theorem to find the length of the top edge.
Let x be the length of the top edge.
Using the Pythagorean theorem in the right triangle formed by the top edge, the slant height, and the difference in height between the left and right edges, we have:
x^2 + 3^2 = 5^2
x^2 + 9 = 25
x^2 = 16
x = 4 (since we are looking for a positive value for the length)
So the length of the top edge is 4 inches.
Now that we know the top edge is also 4 inches, we have a trapezoid with parallel sides of length 4 inches and height 8 inches.
The formula for the area of a trapezoid is:
Area = (1/2) * (sum of parallel sides) * height
Area = (1/2) * (4 + 4) * 8
Area = (1/2) * 8 * 8
Area = 4 * 8
Area = 32 square inches
However, considering the right triangle that was cut off from the original trapezoid (with legs of 3 and 4 inches, and hypotenuse 5 inches), we also need to add that area back to the calculated trapezoid area.
Area of right triangle = (1/2) * base * height
Area of right triangle = (1/2) * 3 * 4
Area of right triangle = 6 square inches
Now, add the areas of the trapezoid and the right triangle:
Total area = 32 + 6
Total area = 38 square inches
So the area of the given trapezoid is 38 square inches.