Calculate Triangle Area: Finding BCD with Side Lengths 12 and 13

Question

Look at the following rectangle:

AAABBBCCCDDD1312

AB = 12

AC = 13

Calculate the area of the triangle BCD.

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Use the Pythagorean Theorem to calculate the length of AD AD .
  • Step 2: Calculate the area of triangle △BCD \triangle BCD .

Step 1: Given AB=12 AB = 12 and AC=13 AC = 13 , we use the Pythagorean Theorem to find AD AD .

AC2=AB2+AD2  ⟹  132=122+AD2 AC^2 = AB^2 + AD^2 \implies 13^2 = 12^2 + AD^2 169=144+AD2  ⟹  AD2=25  ⟹  AD=5 169 = 144 + AD^2 \implies AD^2 = 25 \implies AD = 5

Step 2: Knowing the sides AD=5 AD = 5 (height of the rectangle) and AB=12 AB = 12 (base of the rectangle), triangle △BCD \triangle BCD will have the base BC=12 BC = 12 and the height BD=5 BD = 5 .

The area of triangle △BCD \triangle BCD is:

Area△BCD=12×base×height=12×12×5=30 \text{Area}_{\triangle BCD} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times 5 = 30

Therefore, the area of triangle △BCD \triangle BCD is 30.

Answer

30

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Related Subjects

The Area of a Triangle Area Area of Equilateral Triangles Area of a Scalene Triangle Area of Isosceles Triangles The Pythagorean Theorem Triangle Area of a right triangle Areas of Polygons for 7th Grade How do we calculate the area of complex shapes? How to calculate the area of a triangle using trigonometry? Diagonals in a rectangle

Question Types

Diagonals: Calculation of the diagonal using properties