Answer to part (i): The area of triangle PQR is 10 square cm
Answer to part (ii): in fraction form QM = 5/2, or in decimal form QM = 2.5
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Work Shown for part (i)
One base of triangle PQR is QR = 4
If the base is QR, then the height is PL = 5, which is perpendicular to QR.
area of triangle PQR = (1/2)*base*height
area of triangle PQR = (1/2)*QR*PL
area of triangle PQR = (1/2)*4*5
area of triangle PQR = 10
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Work Shown for part (ii)
Another base for triangle PQR is PR = 8
Imagine rotating triangle PQR so that PR is completely horizontal and flat.
Note: the diagram implies that MR = 8, but instead it's actually PR = 8
For the base PR, the perpendicular height is QM, which we'll label as x for now
area of triangle PQR = (1/2)*base*height
area of triangle PQR = (1/2)*PR*QM
area of triangle PQR = (1/2)*8*x
area of triangle PQR = 4*x
From part (i), we can set 4x equal to 10 since we know the triangle PQR has area 10 square cm.
4x = 10
4x/4 = 10/4
x = 10/4
x = (5*2)/(2*2)
x = 5/2
x = 2.5
