The composite shape's area is 61.12.
Step-by-step explanation:
Step 1; To calculate the value of the composite shapes area we first divide it into shapes whose areas we know. In this case, the composite shape consists of only a circle's half and a triangle attached below it. If we can sum the individual areas of the two shapes we should be able to determine the area of the unknown shape.
Step 2; The triangle has a base length of 8 as it is from (6, 10) to (14, 10) so 14 - 6 = 8 and the height is from (10,10) and (10,1) so the height is 10 -1 = 9. So the area of any given triangle is 0.5 times the product of its base length and height. So area of this triangle = 0.5 × 8 × 9 = 36. The circle is not an entire one but only half so we calculate the entire circle's area and then half it to find its area. The diameter is 8 as the circle's ends are at (6, 10) and (14, 10) and radius = 14 - 6 / 2 = 4. The area of any circle is π times the square of its radius. So area of this circle = π × r²/2= 3.14 × 4²/ 2 = 25.12.
Step 3; Now we calculate the given composite shapes area by summing the two areas i.e areas of the half-circle and the rectangle.
Area of the composite shape = 36 + 25.12 = 61.12.
