Question

Please help, easy geometry​

Answer 1

Answer:

  26 cm²

Step-by-step explanation:

The area of the rectangle whose dimensions are shown at the right and bottom is ...

  (6 cm)(7 cm) = 42 cm²

The figure is smaller than that by the area of the space whose dimensions are shown at the right and in the middle left:

  (4 cm)(4 cm) = 16 cm²

The figure area is then the difference ...

  42 cm² - 16 cm² = 26 cm²

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Alternate solution

Draw a diagonal line between the lower right inside corner and the lower right outside corner. This divides the figure into two trapezoids.

The trapezoid at lower left has bases 7 and 4 cm, and height 6-4 = 2 cm. Its area is ...

  A = (1/2)(b1 +b2)h = (1/2)(7 + 4)(2) = 11 . . . . cm²

The trapezoid at upper right has bases 6 cm and 4 cm and height 3 cm. Its area is ...

  A = (1/2)(b1 +b2)h = (1/2)(6 + 4)(3) = 15 . . . . cm²

Then the area of the figure is the sum of the areas of these trapezoids, so is ...

  11 cm² + 15 cm² = 26 cm²

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Comment on other alternate solutions

There are many other ways you can find the area of this figure. It can be divided into rectangles, triangles, or other figures of your choice. The appropriate area formulas should be used, and the resulting partial areas added or subtracted as required.

You can also let a geometry program find the area for you. (It is 26 cm².)