Solution-1

Denote the altitudes drawn to sides \(BC\) and \(AC\) by \(A A_{1}\) and \(B B_{1}\) (see Fig. 5). Note that \(S_{ABHC}=S_{ABH}+S_{ACH}\).

Using the triangle area formula \(S_{\triangle}=\frac{1}{2} a \cdot h_{a}\), we obtain

\[S_{ABHC}=S_{ABH}+S_{ACH}=\frac{1}{2} AH \cdot BA_{1}+\frac{1}{2} AH \cdot A_{1}C = \frac{1}{2} AH \left(BA_{1}+A_{1}C \right) = \frac{1}{2} AH \cdot BC=\frac{1}{2} \cdot 8 \cdot 8=32.\]

Atrisinājums-1

Pret malām \(BC\) un \(AC\) novilktos augstumus apzīmējam ar \(A A_{1}\) un \(B B_{1}\) (skat. 5.att.).

Ievērojam, ka \(S_{ABHC}=S_{ABH}+S_{ACH}\).

Izmantojot trijstūra laukuma aprēḳināšanas formulu \(S_{\triangle}=\frac{1}{2} a \cdot h_{a}\), iegūstam, ka

\[S_{ABHC}=S_{ABH}+S_{ACH}=\frac{1}{2} AH \cdot BA_{1}+\frac{1}{2} AH \cdot A_{1}C = \frac{1}{2} AH \left(BA_{1}+A_{1}C \right) = \frac{1}{2} AH \cdot BC=\frac{1}{2} \cdot 8 \cdot 8=32.\]