SOHCAHTOA and composite shapes involving circles

Task goals

• Use tangent to derive a shared triangle height and semicircle diameter, then calculate triangle area, semicircle area, and total composite area.
• Use SOHCAHTOA to derive the straight lengths required for both total area and exposed perimeter of a triangle-and-semicircle shape.
• Recognise when a sloping triangle side, rather than its height, is the semicircle diameter and select the required trigonometric ratio.
• Use sine to derive a semicircle diameter when the known triangle height is opposite the marked angle and the diameter is the hypotenuse.
• Calculate the remaining area and exposed perimeter when a quarter circle is cut from a triangle.
• Calculate total area and exposed perimeter when a quarter circle is attached to a triangle.
• Keep full calculator values through multi-step working, then round final lengths and areas to 1 decimal place with correct units.