Find the area of the figure. Hint: Separate into regular shapes and combine the areas! 8 in, 8 in and 8 in

A = [ ? ] in²
Area Formulas: B x H and B x H/2

1 answer

To find the area of the figure with given dimensions of 8 inches, we need to clarify the shape based on the hint to separate it into regular shapes.

Assuming we have an arrangement of three squares, each with dimensions of 8 inches by 8 inches:

  1. Area of each square: \[ A = \text{side} \times \text{side} = 8 , \text{in} \times 8 , \text{in} = 64 , \text{in}^2 \]

  2. Total area of the three squares: \[ \text{Total Area} = 3 \times 64 , \text{in}^2 = 192 , \text{in}^2 \]

Now if we consider that the 8 in, 8 in, and 8 in could represent the sides of a triangle but given as an assumption, let’s consider another method. Assuming we have a triangle formed by these sides:

  1. Area of a triangle using Heron's formula:
    • Calculate the semi-perimeter \(s\): \[ s = \frac{a + b + c}{2} = \frac{8 + 8 + 8}{2} = 12 , \text{in} \]
    • Using Heron's formula to find the area: \[ A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{12(12-8)(12-8)(12-8)} = \sqrt{12 \times 4 \times 4 \times 4} \] \[ A = \sqrt{12 \times 64} = \sqrt{768} = 16 \sqrt{3} \approx 27.71 , \text{in}^2 \]

So based on the visual or a complete description of what the three dimensions form in separation, we can find two figures, either three squares or an equilateral triangle.

The areas calculated are:

  • If three squares: 192 in²
  • If a triangle: approximately 27.71 in²

Without specific indications on the drawing or configuration, please specify if it's forming any unique solid, and we can work with the details further to clarify the total area.