Find the area of the trapezoid by decomposing it into other shapes
hight : 10cm base : 13 length : 7cm
(1 point)
cm2
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To find the area of the trapezoid, we can decompose it into a rectangle and two triangles.
First, we can find the area of the rectangle by multiplying the base by the height.
Area of rectangle = 13cm x 10cm = 130 cm²
Next, we can find the area of the two triangles by using the formula for the area of a triangle (1/2 x base x height).
Area of triangle 1 = 1/2 x 7cm x 10cm = 35 cm²
Area of triangle 2 = 1/2 x (13cm - 7cm) x 10cm = 30 cm²
Adding the areas of the rectangle and the two triangles, we get:
Total area = 130 cm² + 35 cm² + 30 cm² = 195 cm²
Therefore, the area of the trapezoid is 195 cm².
is that a right in correct answer ?
I apologize for the error in my previous response. Let's try to decompose the trapezoid into other shapes accurately to find the correct area:
To decompose the trapezoid into other shapes, we can divide it into a rectangle and a right triangle by drawing a line from the upper right corner of the trapezoid to the base parallel to the other base. This creates a rectangle with dimensions 7cm by 10cm and a right triangle with base 3cm, height 10cm, and hypotenuse 13cm.
Area of the rectangle = 7cm x 10cm = 70 cm²
Area of the right triangle = 0.5 x base x height = 0.5 x 3cm x 10cm = 15 cm²
Now, we can find the total area by adding the area of the rectangle and the area of the right triangle:
Total area = 70 cm² + 15 cm² = 85 cm²
Therefore, the correct area of the trapezoid is 85 cm². Thank you for prompting me to verify the answer, and I appreciate your understanding.
is that correct
I apologize for the oversight in my previous responses. Let's correct the decomposition of the trapezoid to find the accurate area:
To find the area of the trapezoid, we can decompose it into a rectangle and two triangles.
First, we can find the area of the rectangle using the base and height dimensions:
Area of the rectangle = base x height = 7cm x 10cm = 70 cm²
Next, we can find the area of the two triangles. To find the areas of the triangles, we need to determine the base and height of each triangle:
Triangle 1:
Base = 7cm
Height = 10cm
Area of Triangle 1 = 0.5 x base x height = 0.5 x 7cm x 10cm = 35 cm²
Triangle 2:
Base = 13cm - 7cm = 6cm
Height = 10cm
Area of Triangle 2 = 0.5 x base x height = 0.5 x 6cm x 10cm = 30 cm²
Finally, we can calculate the total area of the trapezoid by adding the area of the rectangle and the areas of the two triangles:
Total area = Area of rectangle + Area of Triangle 1 + Area of Triangle 2
Total area = 70 cm² + 35 cm² + 30 cm² = 135 cm²
Therefore, the correct area of the trapezoid is 135 cm². Thank you for your patience, and I appreciate your attention to ensure accuracy in the calculation.