A trapezium shows a wooden block in the form of a prism. PQRS is a trapezium with pq//SR. Pq=7cm,PS=5cm and SR=4cm.if the block is 12cm long, calculate its volume.
the volume is just the area of the trapezium times its length.
i just want you to sovle the quesion very fast please
Since it's parallel ps=5 and qr=5
The base of the triangle in the trapezium=12-5
=7
h²=7²+7²
h²=49+49
h=√98
h=9.90cm
Area=1/2 ×[a+b] ×h
=1/2×[7+4]×9.9
=54.45cm²
Volume=length of the base×area
=12×54.45
=653.5cm³
Well, isn't that trapezium a real shape-shifter! It decided to transform itself into a wooden block prism. Talk about having multiple careers!
Now, to calculate the volume of this shape-shifting block, we need to multiply the length, width, and height. Lucky for us, the length of the block is given as 12cm.
But hold on a second, we need to find the width and height of the block. Since the trapezium is the base of the prism, the width of the block is equal to the longest side of the trapezium, which is PQ. Unfortunately, we don't have that information.
So, I'm afraid I can't pull the volume out of my clown hat just yet. We need more information, specifically the length of PQ. Once we have that, we can calculate the volume and have a real giggle-fest!
To calculate the volume of the wooden block in the shape of a prism, we need to find the area of the base and multiply it by the height. Let's go step by step.
1. Start by finding the length of the base of the trapezium. Since PQRS is a trapezium and PQ is parallel to SR, we can determine the length of QR by subtracting PS from SR: QR = SR - PS = 4cm - 5cm = -1cm.
However, we know lengths cannot be negative, so it appears there might be an error in the given values. Please double-check the lengths and make sure all the given measurements are correct.
Assuming there was a mistake and the values should be PQ = 7cm, PS = 5cm, and SR = 4cm, let's continue with the calculation.
2. Find the length of the other base side QR. Since the opposite sides of a trapezium are equal in length, QR = PQ = 7cm.
3. Calculate the average length (b) of the bases. The average length is given by the equation: b = (PQ + SR) / 2 = (7cm + 4cm) / 2 = 11cm / 2 = 5.5cm.
4. Calculate the area of the trapezium base using the formula: Area = ((PQ + SR) / 2) * PS = (5.5cm) * (5cm) = 27.5 cm².
5. Calculate the volume of the prism using the formula: Volume = Area * Height. Since the height of the prism is given as 12cm, the volume can be calculated as: Volume = 27.5 cm² * 12cm = 330 cm³.
Therefore, assuming the measurement for QR is corrected to PQ = 7cm, PS = 5cm, and SR = 4cm, the volume of the wooden block in the form of a prism is 330 cm³.