Answer:
10 square centimeters
Step-by-step explanation:
The figure can be decomposed into four triangles and one smaller square. The area is the sum of the areas of those parts.
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The attachment shows how the square can be decomposed into a 2×2 square and four 3×1 triangles. The four triangles are equivalent in area to two 3×1 rectangles.
The area of each rectangle/square is the product of its dimensions.
total area = square area + rectangle area
total area = 2×2 + 2×(3×1) = 4 + 6 = 10 . . . . . square cm
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Additional comment
Other ways you can arrive at the area are ...
➤ Use the Pythagorean theorem to find the length of a side. Each side is the hypotenuse of a right triangle with legs 3 and 1, so the square of the hypotenuse (and the area of this square) is ...
c² = A = a² +b² = 3² +1² = 9 +1 = 10 . . . . square cm
➤ Use the Pythagorean theorem to find the length of a diagonal. Each diagonal of this square is the hypotenuse of a right triangle with legs 2 and 4. The square of the diagonal is twice the area of the square in the picture.
c² = 2A = a² +b² = 2² +4² = 4 +16 = 20
A = 20/2 = 10 . . . . square cm
➤ Find the area of the enclosing square, and subtract the missing triangle corners.
A = 4² - 4×(1/2(3)(1)) = 16 -6 = 10 . . . . square cm
