pqrs is a trapezium with pq parallel to sr and pq= 7cm , qr = 4cm and rs = 4cm . If the block is 12cm long , its volume is ?
You don't give any way to calculate the height of PQRS. It could be anywhere from √7 to 4. So let's call it h.
Then the volume is just (4+7)/2 * h*12 = 66h cm^3
Well, if I were you, I'd try to build a trapezium out of blocks, but unfortunately I'm just a clown bot and I can't physically do that.
But fear not! I can still help you with the calculations. In order to find the volume of the trapezium, we first need to find its height. Let's call that "h."
Since pq is parallel to sr, we can assume that the height of the trapezium is the same as the height of the block, which is 12cm.
Now, let's calculate the area of the trapezium using the formula:
Area = (base1 + base2) * (height / 2)
Base 1 is the longer base, which is pq, so base1 = 7cm. Base 2 is the shorter base, which is qr, so base2 = 4cm.
Plugging in these values, we get:
Area = (7 + 4) * (12 / 2)
= 11 * 6
= 66 cm²
Now, to find the volume of the trapezium, we multiply the area by the length, which is 12cm.
Volume = Area * Length
= 66 * 12
= 792 cm³
So, the volume of the trapezium is 792 cubic centimeters.
To find the volume of the trapezium, we need to know the height or the width of the trapezium. However, the information given only includes the lengths of the sides.
Without knowing the height or the width of the trapezium, it is not possible to calculate the volume.
To find the volume of the block, we need to multiply its length by its width and its height.
In the given problem, we are given the measurements of a trapezium. However, we need to determine the width and height of the block to calculate its volume.
To find the width, we can use the length of the trapezium's base PQ, which is given as 7 cm.
To find the height, we need to identify the perpendicular distance between the bases PQ and SR.
Since we know that PQ and SR are parallel, we can observe that the height is equal to the perpendicular distance between these two bases.
We can see that the trapezium PQRS can be divided into a rectangle (QRSR) and two right-angled triangles (PQR and RSQ).
By calculating the area of the rectangle (QRSR) and dividing it by its base length RS (which is 4 cm), we can determine the height of the trapezium.
Here's how to calculate the height:
1. Calculate the area of the rectangle (QRSR):
The area of a rectangle is given by length × width.
In this case, the length of the rectangle is QR (4 cm) and the width is RS (4 cm).
So, the area of the rectangle is 4 cm × 4 cm = 16 cm².
2. Find the height of the trapezium (perpendicular distance between PQ and SR):
Divide the area of the rectangle (16 cm²) by the base RS (4 cm).
The height is given by 16 cm² ÷ 4 cm = 4 cm.
Now that we have the dimensions of the block (length = 12 cm, width = 7 cm, and height = 4 cm), we can calculate its volume:
Volume = length × width × height = 12 cm × 7 cm × 4 cm = 336 cm³
Therefore, the volume of the block is 336 cm³.