To find the area of the shape below, we need to split it into two triangles and a rectangle, then find the area of each shape and add them together.
First, we'll split the shape as shown:
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|\ /|
| \ / |
| \ / |
| X |
| / \ |
| / \ |
|/ \|
+-----------+-------+-----------+
6 cm 9 cm 15 cm
The rectangle has a length of 15 cm and a width of 6 cm, so its area is:
Area of rectangle = length x width = 15 cm x 6 cm = 90 cm²
To find the area of the two triangles, we need to first find the height of each triangle. We can use the Pythagorean theorem to find the height:
For the triangle on the left:
h = sqrt(11^2 - 6^2) = sqrt(121 - 36) = sqrt(85) ≈ 9.22 cm
For the triangle on the right:
h = sqrt(9^2 - 6^2) = sqrt(81 - 36) = sqrt(45) ≈ 6.71 cm
The area of each triangle is then:
Area of triangle = 1/2 x base x height
For the triangle on the left:
Area of triangle = 1/2 x 11 cm x 9.22 cm ≈ 50.66 cm²
For the triangle on the right:
Area of triangle = 1/2 x 9 cm x 6.71 cm ≈ 30.195 cm²
Finally, we add the areas of the rectangle and the two triangles together:
Total area = area of rectangle + area of triangle on the left + area of triangle on the right
Total area = 90 cm² + 50.66 cm² + 30.195 cm² ≈ 170.855 cm²
Therefore, the area of the given shape is approximately 170.855 cm².