Question

Area of 6ft 10ft 14ft figure

Answer 1

209.25

Explanation:

Calculate the areas of the triangle, rectangle, and half circle, then add them together:

triangle = 1/2bh = 1/2(6)(10) = 30

rectangle = bh = (14)(10) = 140

half circle = 1/2πr² = 1/2(3.14)(5)² = 39.25

radius = r = D/2 = 10/2 = 5

Total area = 30 + 140 + 39.25 = 209.25

Answer 2

209.25 ft²

Explanation:

To find the total area of the figure you have to add the areas of the triangle, rectangle and the semi circle.

Area of the triangle.

`\sf \: A = (1)/(2) * base * height \\ \sf \: A = (1)/(2) * 6 \: ft *10 \: ft \\ \sf \: A = (1)/(2) * 60 \: {ft}^(2) \\ \sf \: A =30 \: {ft}^(2)`

Area of the rectangle.

`\sf \: A =length * width \\ \sf \: A =14 \: ft * 10 \: ft \\ \sf A =140 \: {ft}^(2)`

Area of the semi circle.

`\sf \: A = (1)/(2) \pi {r}^(2) \\ \sf \: A = (1)/(2) * \pi * ( (10)/(2)) ^(2) \\ \sf \: A = (1)/(2) * \pi * {5}^(2) \\ \sf \: A = (1)/(2) * \pi * 25 \\ \sf \: A = (1)/(2) * 3.14 * 25 \\ \sf \: A = (1)/(2) * 78.5 \\ \sf \: A = 39.25 {ft}^(2)`

Add up all the areas to find the total area.

`\sf \: Total \: Area = 30 {ft}^(2) + 140 {ft}^(2) + 39.25 {ft}^(2) \\ = 209.25 {ft}^(2)`