Question

1.2 m

1.2 m
Susie is 1.13 metres tall
She has a play tent in the shape of a triangular prism.
The diagram shows the front view of the tent.
The front of the tent has been drawn to scale below.
a) Complete the scale drawing.
1.5m
Not drawn accurately
b) Can Susie stand up in the
middle of the tent?
1.5m
Scale: 1 cm represents 60 cm

Answer 1

The height of the tent is smaller than the height of Suzie so she cannot stand up.

How to calculate the height of the tent?

To calculate the height of the tent, the following steps should be taken as follows:

The triangular prism tent is divided into two right triangles using an imaginary line.

The middle height can be calculated using the Pythagorean formula.

c² = a²+b²

1.2²= 0.75²+ b²

b² = 1.2²-0.75²

= 1.44-0.5625

= 0.8775

b = √0.8775

= 0.88m

Since Susie is 1.13m tall, she cannot stand up on the tent that is just 0.88m high.

Answer 2

Split the triangle into 2 right in the middle so you have 2 identical right triangles. The base on one would be half the base of the triangle shown so, the base would be: 1.5/2 = 0.75 m.

Now using the Pythagorean theorem you can find the height:

Height - sqrt(1.2^2 - 0.75^2)

Height = sqrt(1.44 - 0.5625)

Height = sqrt(0.8775)

Height = 0.93675 meters

The height of the tent is smaller than the height of Suzie so she cannot stand up.