AMC 8 Daily Practice - Pythagorean Theorem

Complete problem set with solutions and individual problem pages

Problem 4 Easy

As shown in the figure, there is a lawn. It is known that AD = 12m, CD = 9m, AB = 39m, BC = 36m, and \angle ADC = 90^\circ. Find the area of this lawn.

  • A.

    160

  • B.

    189

  • C.

    216

  • D.

    245

  • E.

    270

Answer:C

Connect AC.

Since \angle ADC = 90^\circ, in the right triangle ACD: AC = \sqrt{DA^2 + DC^2} = 15 m.

Given AB = 39m and BC = 36m, we find that BC^2 + AC^2 = AB^2, so \triangle ABC is also a right triangle.

The area of the lawn is: \text{Area of } \triangle ABC - \text{Area of } \triangle ACD = \frac{1}{2} \times 36 \times 15 - \frac{1}{2} \times 12 \times 9 = 270 - 54 = 216 \text{ square meters}

Related Problems
Problem 2 AMC 8 Daily Practice - Pythagorean Theorem
Problem 3 AMC 8 Daily Practice - Pythagorean Theorem
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Problem 6 AMC 8 Daily Practice - Pythagorean Theorem
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