AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 6 Easy

A trapezoid has a top base of length 5, a bottom base of length 10, and two legs of lengths 3 and 4, respectively. What is the area of the trapezoid?

  • A.

    18

  • B.

    22.5

  • C.

    26.25

  • D.

    30

  • E.

    32

Answer:A

As shown in the diagram, draw AE \parallel BC through point A, intersecting DC at point F. Draw AF \perp DC at point F.

Since quadrilateral ABCE is a parallelogram, we have:   AE = BC = 4

Also,   DE = DC - AB = 10 - 5 = 5

Given that AD = 3, applying the Pythagorean theorem in right triangle \triangle ADE, we find:   AF = \frac{3 \times 4}{5} = 2.4

Thus, the area of trapezoid ABCD is:   S_{ABCD} = \frac{(5+10) \times 2.4}{2} = 18

Related Problems
Problem 4 AMC 8 Daily Practice Round 9
Problem 5 AMC 8 Daily Practice Round 9
Problem 7 AMC 8 Daily Practice Round 9
Problem 8 AMC 8 Daily Practice Round 9
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