Answer:
- smaller quadrilateral: 8
- larger quadrilateral: 13 1/3
Explanation:
Suppose the base and height of the given triangle are represented by "b" and "h". Then the area of that triangle is ...
A = (1/2)bh = 24 . . . . . . given
bh = 48 . . . . . . . . . . . . . multiply by 2
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Now the larger quadrilateral is a trapezoid with height h/3 and bases b and (2/3)b. Its are will then be ...
A = (1/2)(b1 +b2)h = (1/2)(b +(2/3)b)(1/3h) = 1/6·5/3·bh
Substituting the above value of bh, we find ...
area of larger quadrilateral = (5/18)(48) = 40/3 = 13 1/3
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In similar fashion, the smaller quadrilateral is a trapezoid with bases 2/3b and 1/3b and height 1/3h. Its area is then ...
A = (1/2)(2/3b +1/3b)(1/3h) = 1/6·bh
As before, substituting the value of bh, we find ...
area of smaller quadrilateral = (1/6)(48) = 8
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A geometry application confirms these values.