Geometry

According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the legs. Solving 5^2 + b^2 = 13^2 yields b^2 = 144, meaning the missing leg is 12. Option A is incorrect because it is the result of simply subtracting 5 from 13, which violates the geometric relationship.

The area of a triangle is calculated using the formula: area equals half the product of the base and height.. The area of a triangle is (1/2)·base·height; substituting base = 8 and height = 5 gives 0.5 × 8 × 5 = 20 square units.

The correct answer is 20 because it is calculated using the formula for the area of a triangle, which is half the product of the base and height. Trace the diagram above to fix how the pieces of Geometry fit together.

• !A common mistake is to forget the 1/2 factor in the area formula, leading to an area that is twice as large as it should be. This mistake would result in choosing answer 40 instead of the correct answer 20.
• !Many people incorrectly calculate the perimeter of a hexagon by treating it as a combination of a square and an equilateral triangle, which can lead to incorrect answers.
• !Option A is incorrect because 16 represents the perimeter of a square with side length 4, rather than a six-sided hexagon.
• !Option A is incorrect because it fails to square the radius, multiplying only 3 by 7.
• !Option A is incorrect because it is the result of simply subtracting 5 from 13, which violates the geometric relationship.

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Run a focused 10-question mini-mock on Geometry and see it stick.