CIE Mathematics Paper-1: Specimen Questions 40 - 41 of 175

Question number: 40

Short Answer Question▾

Write in Short

In the right-angled triangle ABC, BC = 4 cm and angle C=450 . Calculate the length of AB and AC.

A right angled triangle has an angle and length of a side

A right angled triangle has an angle and length of a side

Find the length of side AB and diagonal AC of triangle ABC by using given values

Explanation

Here, triangle ABC is right angled triangle,

Angle BAC=450 and BC = 4 cm is given,

So, tan450=BCAB1=4ABAB=4cm.

Now, sin450=BCAC0.707=4ACAC=40.707AC=5.66cm

Question number: 41

Essay Question▾

Describe in Detail

The diagram shows two triangles of side 10 cm and height 9 cm and three congruent rectangles with two sides of 12 cm.

Two triangles and three congruent rectangles

Two triangles and three congruent rectangles

Find the below given calculations by using given values of rectangles and triangles

(a) Calculate

(i) The area of one rectangular face,

(ii) The area of the whole shape.

(b) What is the shape known as? This shape is the net of a solid.

Explanation

Here,

(a) (i) The area of rectangle: w×l , where, w = width and l = length.

So, here, width w = 10 cm and length l = 12 cm

So, area of one rectangular face = w×l=10×12=120cm2

(ii) The area of whole shape = (3×areaofonerectangularface)+(2×areaofonetriangle)

So, area of triangle = hb2 where, h = height and b = base.

So, here, height h = 9 cm and base will be the width of rectangle base b = 10 cm

So, area of one triangular face = hb2=10×92=45cm2

Thus, area of whole shape = (3×120)+(2×45)=360+90=450cm2

(b) The shape is the net of a solid. So, it is called as Triangular Prism.

  • If there are equilateral triangles bases and square sides then the prism is called as Uniform Triangular Prism.
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