Question

Find the area of a rhombus each side of which measure 20cm and one of whose diagnal is 24cm

Answer 1

Answer:

$\huge{\red{\boxed{\boxed{\green{\sf{AREA=312cm^{2}}}}}}}$

Step-by-step explanation:

$\huge{\red{\boxed{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}}$

□Side= 20cm

□Diagonal= 24cm

To find:

○Area of rhombus

$we \: know \: the \: properties \: of \: rhombus \\ (1)all \: sides \: are \: equal \\ (2)diagonals \: bisects \: each \: other \: at \: 90 \degree \\ (3)area \: of \: rhombus = \frac{1}{2} \times d1 \times d2 \\ \\ according \: to \: these \: information \: \\ first \: we \: find \: d2 \\ side(hypotenuse) = 20cm \\ d1 = 24cm \\ so \: perpendicular \: = 12cm \\ \\ {h}^{2} = {p}^{2} + {b}^{2} \\ = ) {20}^{2} = {12}^{2} + {b}^{2} \\ = )400 - 144 = {b}^{2} \\ = ){b }^{2} = 256 \\ = ) b = \sqrt{256} \\ = )b = 13cm \\ \\ d2 = 2 \times b = 2 \times 13 = 26cm \\ \\ area \: of \: rhombus = \frac{1}{2} \times d1 \times d2 \\ = ) \frac{1}{2} \times 24 \times 26 \\ = )12 \times 26 \\ = )312cm^{2}$

$\huge{\red{\boxed{\boxed{\green{\sf{AREA=312cm^{2}}}}}}}$

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Answer 2

Answer:

A = 384cm²

a = Side = 20cm

p = Diagonal = 24 cm

a = pq / 2

a = p² + q² / 2

a = 1 / 2 p √4² - p²

= 1 / 2 • 24 • √ 4.20² - 24² = 384 cm³