Answer:
72 square inches
Explanation:
You have a kite with orthogonal diagonals, both of length 12 inches, and you want the area.
Area formula
The area of a quadrilateral with orthogonal diagonals (typically, a kite or rhombus) is given by the formula ...
A = 1/2(d1)(d2)
For diagonals of length 12 in, the area is ...
A = 1/2(12 in)(12 in) = 72 in²
The area of the kite is 72 square inches.
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Additional comment
If you like, you can add the areas of the four triangles. Let d1 = d1a +d1b, the two segment lengths of the diagonal. Similarly, let d2 = d2a +d2b. Then the area of the figure is the sum of the areas of the four triangles:
A = 1/2(d1a·d2a) +1/2(d1b·d2a) +1/2(d1a·d2b) +1/2(d1b·d2b)
= 1/2(d1a +d1b)(d2a +d2b) = 1/2(d1)(d2) . . . . as above
Orthogonal = "meets at right angles"