SP001 Maths Paper 2 - Question 12

The figure below shows a triangle ABC drawn on a square grid.

a) Find the area of Triangle ABC.
Ans: ______________$cm²$ [1]

b) Draw an isosceles triangle PQR on the square grid below.
The ratio of the area of isosceles PQR to the area of the above triangle ABC is 8 : 15.

(For the purpose of this online test, calculate the base, height and area of the isosceles PQR.
If it would help you better visualise the triangles, you may wish to print out this page or do the problem on an exercise book or paper with square boxes.)

Ans: Base	= ______________$cm$ [1]
Height	= ______________$cm$ [1]
Area	= ______________$cm²$ [1]

Answer

maxloo · 26 Jun 2026, 19:45 · official answer

(a)

Area of ABC	= $\dfrac{1}{2}$ $\times$ $5$ $\times$ $6$
	= $\boxed{15\ cm²}$

(b)

Area of triangle PQR	= $\dfrac{8}{15}$ $\times$ $15$
	= $\boxed{8\ cm²}$

Assume isosceles triangle PQR is a right-angled triangle,

where base PQ	= height QR
$\Rightarrow$ Area of triangle PQR	= $\dfrac{1}{2}$ $\times$ base PQ $\times$ height QR = 8
base PQ $\times$ base PQ	= $16$
Hence, PQ	= $\boxed{4\ cm}$ = QR