Question

on the set of axes below, rhombus abcd has vertices whose coordinates are a(1,2), b(4,6), c(7,2), and d(4,-2). find the area of the rhombus. (hint... break the rhombus up into triangles)
○ 28
○ 34
○ 48
○ 20

Explanation:

Step1: Split rhombus into 4 triangles

We can divide rhombus ABCD into 4 right triangles by drawing the diagonals (connecting A to C, B to D).

Step2: Find base/height of 1 triangle

For one triangle: base = $\frac{7-1}{2}=3$, height = $\frac{6-(-2)}{2}=4$

Step3: Calculate area of 1 triangle

Area of 1 triangle: $\frac{1}{2} \times 3 \times 4 = 6$

Step4: Calculate total area of rhombus

Total area = $4 \times 6 = 24$

Answer:

24 (the corresponding option is the second one: $\boldsymbol{24}$)