Help please. I don’t understand and my teacher didn’t bother to teach us any of this and my brain hurts

  23.  42 m^2

  24.  144 ft^2

  25.  68 cm^2

Step-by-step explanation:

The teacher should not need to spend any time teaching this. The area of the total figure is the sum of the areas of its parts. You already know that. And, you already know how to compute the areas of triangles and rectangles.

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You may recall that the area of a triangle is ...

  A = 1/2bh

and the area of a rectangle with the same base and height is ...

  A = bh

So, a triangle with base b and height h has the same area as a rectangle with the same base (b) and half the height (h/2). Recognizing this makes these problems really simple.

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23. The base of the rectangle and triangle is 7 m. The height of the triangle is 4 m, so its area is equivalent to adding 4/2 = 2 m to the 4 m height of the rectangle. Then the total area is ...

  A = (7 m)(4 m +(1/2)(4 m)) = (7 m)(6 m) = 42 m^2

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24. Since there are two identical triangles of height 5, their total area is equal to that of a rectangle of height 5.

  A = (12 ft)(7 ft +5 ft) = 144 ft^2

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25. The 5 cm height of the triangle makes it have an area equivalent to a rectangle 5/2 cm high.

  A = (8 cm)(6 cm +5/2 cm) = 68 cm^2

Note: we have read the fuzzy numbers as 8 cm wide, 6 cm high for the rectangle, and 5 cm high for the triangle. If your figure is different, please use the appropriate numbers in the calculation.

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