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in exact form: 291.5 + 30.25π cm²

              correct to 2 decimal places: 386.53 cm²

Step-by-step explanation:

first you find the area of the rectangle:

= length × width

= 53 × 11

= 583 cm²

Next you find the area of the semicircle:

= π × r² (where r is the radius)

= π × (11/2)²

= 30.25π cm²

Then you find the area of the unshaded triangle:

= half × base length × perpendicular height

= 1/2 × 53 × 11

=291.5 cm²

Finally you subtract the unshaded area (the triangle) from the shaded area (not including the semicircle) then add the semicircle to your result.

= 583 (rectangle) - 291.5 (triangle) + 30.25π (semicircle)

= 291.5 + 30.25π

≈ 386.53 cm² (2 decimal places)