Name: Volume of 3D Shapes
Uploaded: 2019-07-19
Duration: 7 min 3 s
Description: Here's how to calculate the three-dimensional volume that the shape will occupy. This is like the amount of water that a shape could hold if it was hollow.

Question

Calculate the area of the pentagon $A B C D E$ shown in figure below, given that $A X = B X = 6 cm, E Y = C Y = 4 cm, D E = D C = 5 cm D X = 9 cm$ and DX is perpendicular to EC and AB .

Accepted Answer

Here $A B C D$ is the pentagon,

Given that

$A X = B X =$ $6 cm,$ $E Y = C Y = 4 cm$

$D E = D C = 5 cm$

$D X = 9 cm$

And $D X$ is perpendicular to $E C and A B$

In triangle $D E Y$ ,

By Pythagoras theorem,

$D E^{2} = D Y^{2} + E Y^{2} 5^{2} = D Y^{2} + 4^{2} D Y = 3 c m$

Area of pentagonal field $A B C D E =$ area of triangle $D E Y +$ area of triangle $D C Y +$ area of trapezium $E Y X A +$ area of trapezium $C Y X B$

$= \frac{1}{2} \times$ base $\times$ height $+ \frac{1}{2} \times$ base $\times$ height $+ \frac{1}{2} \times$ (sum of parallel sides) $\times$ height $+ \frac{1}{2} \times$ (sum of parallel sides) $\times$ height $= \frac{1}{2} \times E Y \times D Y + \frac{1}{2} \times C Y \times D Y + \frac{1}{2} \times (E Y + A X) \times X Y + \frac{1}{2} \times (C Y + B X) \times X Y$

$= \frac{1}{2} \times 4 \times 3 + \frac{1}{2} \times 4 \times 3 + \frac{1}{2} \times (4 + 6) \times (D X - D Y) + \frac{1}{2} \times (4 + 6) \times (D X - D Y) = 6 + 6 + \frac{1}{2} \times 10 \times (9 - 3) + \frac{1}{2} \times 10 \times (9 - 3) = 6 + 6 + 30 + 30 = 72 sq . m$

Calculate the area of the pentagon $A B C D E$ shown in figure below, given that $A X = B X = 6 cm, E Y = C Y = 4 cm, D E = D C = 5 cm D X = 9 cm$ and DX is perpendicular to EC and AB .

Important Questions on Mensuration

Learn and Prepare for any exam you want !

Calculate the area of the pentagon ABCDE shown in figure below, given that AX = BX = 6 cm, EY = CY = 4 cm, DE = DC = 5 cm DX = 9 cm and DX is perpendicular to EC and AB .

Important Questions on Mensuration

Learn and Prepare for any exam you want !

Calculate the area of the pentagon $A B C D E$ shown in figure below, given that $A X = B X = 6 cm, E Y = C Y = 4 cm, D E = D C = 5 cm D X = 9 cm$ and DX is perpendicular to EC and AB .