Question

the formula for finding the area of a rhombus or kite is area = \\( \frac { 1 } { 2 } \times \\) diagonal 1 \\( \times \\) diagonal 2. this is written as \\( a = \frac { 1 } { 2 } \times d _ { 1 } \times d _ { 2 } \\) or \\( a = \frac { 1 } { 2 } d _ { 1 } d _ { 2 } \\). example: \\( a = \frac { 1 } { 2 } \times d _ { 1 } \times d _ { 2 } \\) \\( a = \frac { 1 } { 2 } \times 12 \times 9 \\) \\( a = 54 m ^ { 2 } \\) find the area of each rhombus or kite. a. area: _ b. area: _ c. d.

Explanation:

Step1: Apply the area formula for a.

For the rhombus/kite in a, \(d_1 = 16\) in and \(d_2=11\) in. Use \(A=\frac{1}{2}d_1d_2\).
\(A=\frac{1}{2}\times16\times11\)
\(A = 8\times11\)
\(A=88\) in²

Step2: Apply the area formula for b.

For the rhombus/kite in b, \(d_1 = 8\) cm and \(d_2 = 19\) cm. Use \(A=\frac{1}{2}d_1d_2\).
\(A=\frac{1}{2}\times8\times19\)
\(A = 4\times19\)
\(A = 76\) cm²

Step3: Apply the area formula for c.

For the rhombus/kite in c, \(d_1=13\) mm and \(d_2 = 20\) mm. Use \(A=\frac{1}{2}d_1d_2\).
\(A=\frac{1}{2}\times13\times20\)
\(A=13\times10\)
\(A = 130\) mm²

Step4: Apply the area formula for d.

For the rhombus/kite in d, \(d_1 = 90\) ft and \(d_2=240\) ft. Use \(A=\frac{1}{2}d_1d_2\).
\(A=\frac{1}{2}\times90\times240\)
\(A = 45\times240\)
\(A=10800\) ft²

Answer:

a. \(88\) in²
b. \(76\) cm²
c. \(130\) mm²
d. \(10800\) ft²