Find radius of a circle having the same area as that of trapezium as s

1.	Find radius of a circle having the same area as that of trapezium as shown in the figure.Height of the trapezium is 4 times Pi. Please give full solution and I will mark u as brainliest if u did
Answer» align="ABSMIDDLE" alt="\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge{\boxed{\bullet{\red{\MATHBB{ANSWER}}}\bullet}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:" CLASS="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5Chuge%7B%5Cboxed%7B%5Cbullet%7B%5Cred%7B%5Cmathbb%7BANSWER%7D%7D%7D%5Cbullet%7D%7D%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A" title="\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge{\boxed{\bullet{\red{\mathbb{ANSWER}}}\bullet}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:"> First we will find out the are of trapezium given :- AB = 18 DC = 32 Distance between parallel LINES (h) = 4π Area of trapezium = $\frac{1}{2}$ × ( Sum of parallel sides ) × h ✒ $\frac{1}{2}$ × ( AB + DC ) × h ✒ $\frac{1}{2}$ ×(18+32) × 4π ✒ $\frac{1}{2}$ × 50 × 4π ✒ 25 × 4π ✒ 100π Now, ✯ Area of circle = Area of trapezium ➙ πr² = 100π ➙ π × r × r = 100 × π ➙ cancelling 'pi' (π) from both sides ➙ r² = 100 ➙ r = $\sqrt{100}$ ➙ r = 10 ∴ *Radius of the circle = 10*

Find radius of a circle having the same area as that of trapezium as shown in the figure.Height of the trapezium is 4 times Pi. Please give full solution and I will mark u as brainliest if u did

Answer»

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First we will find out the are of trapezium given :-

AB = 18

DC = 32

Distance between parallel LINES (h) = 4π

Area of trapezium = $\frac{1}{2}$ × ( Sum of parallel sides ) × h

✒ $\frac{1}{2}$ × ( AB + DC ) × h

✒ $\frac{1}{2}$ ×(18+32) × 4π

✒ $\frac{1}{2}$ × 50 × 4π

✒ 25 × 4π

✒ 100π

Now,

✯ Area of circle = Area of trapezium

➙ πr² = 100π

➙ π × r × r = 100 × π

➙ cancelling 'pi' (π) from both sides

➙ r² = 100

➙ r = $\sqrt{100}$

➙ r = 10

∴ Radius of the circle = 10