The diagram shows a shape made from triangle 𝐴𝐵𝐶 and a semicircle with diameter 𝐵𝐶.Triangle 𝐴𝐵𝐶 is right-angled at 𝐵.𝐴𝐵=7.6 cm and 𝐴𝐶=9.5 cm.Calculate the area of the shape.Give your answer correct to 3 significant figures.

To find the area of the shape, we need to calculate the area of the triangle ABC and the area of the semicircle separately, then add them together.

Step 1: Calculate the area of triangle ABC The area of a right-angled triangle is given by the formula 1/2 * base * height. Here, AB is the base and AC is the height. So, Area of triangle ABC = 1/2 * AB * AC = 1/2 * 7.6 cm * 9.5 cm = 36.2 cm²

Step 2: Calculate the area of the semicircle The area of a circle is given by the formula πr², where r is the radius. The radius of the semicircle is half of BC. Since ABC is a right-angled triangle, BC (the hypotenuse) can be found using Pythagoras' theorem: BC = sqrt(AB² + AC²) = sqrt((7.6 cm)² + (9.5 cm)²) = 12.21 cm. So, the radius of the semicircle is 12.21 cm / 2 = 6.105 cm. The area of the semicircle is then 1/2 * π * (radius)² = 1/2 * π * (6.105 cm)² = 58.672 cm²

Step 3: Add the areas of the triangle and the semicircle Total area = Area of triangle ABC + Area of semicircle = 36.2 cm² + 58.672 cm² = 94.872 cm²

So, the area of the shape is approximately 94.9 cm², to three significant figures.