Math Problem Statement

Jawab

Tentukan panjang sisi AB pada tiap bangun berikut (Find the length of side AB), Tentukan luas tiap bangun berikut (Find the area of the shapes), Kelompok bilangan manakah yang merupakan ukuran segitiga siku-siku? (Which group of numbers represents a right triangle?)

Solution

Let's work through the questions from the image you uploaded.

Question 1: Tentukan panjang sisi AB pada tiap bangun berikut (Find the length of side AB in the following shapes)

a) For the first shape (right triangle):

  • Sides: AC = 6 cm (base), BC = 15 cm (hypotenuse), height from C to AB = 10 cm
  • Use the Pythagorean theorem to find AB. AB2=AC2+BC2=62+102=36+100=136AB^2 = AC^2 + BC^2 = 6^2 + 10^2 = 36 + 100 = 136 AB=13611.66cmAB = \sqrt{136} \approx 11.66 \, \text{cm}

b) For the second shape (triangle):

  • Given: AE = 12 cm (height), AB = 20 cm (hypotenuse), BE = 12 cm (vertical height), CE = 15 cm
  • Again using the Pythagorean theorem, solve for AB. AB=AE2+BE2AB = \sqrt{AE^2 + BE^2} which gives

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Math Problem Analysis

Mathematical Concepts

Geometry
Pythagorean Theorem
Area Calculation

Formulas

Pythagorean theorem: a² + b² = c²
Area of a trapezoid: A = 1/2 × (Base1 + Base2) × Height
Area of a diamond: A = 1/2 × Diagonal1 × Diagonal2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-8